Use definitions of right-hand and left-hand limits to prove the limit statement.lim-1|x|X>0Since x approaches 0 from the left, x<0, (x = []).
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First we need to understand what |x| means or what values it repressents
[tex]|x|=\begin{cases}x,x\ge0 \\ \\ -x,x<0\end{cases}[/tex]|x| indicates the absolute value of x, this is, x is always going to be positive, for example,
when x = 1 -> |x| = 1 , but also when x = -1 , then |x| = 1
Since, in this case, we need to find the limit when X approaches 0 from the left we are going to use |x| = -x , for x<0
this is...
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}=\lim _{x\rightarrow0-}(-1)=-1[/tex]At this point we have proved the limit statement.
So, in order to answer the question in the lower part... x approaches to 0 from the left, x<0, |x| = -x
In the graph you can see, whenever X<0 the value of the funcion will be negative and when it approaches 0 it becomes -1
On the other hand, when the function approaches to 0 from the right, the value of the function is +1. This is a discontinuity
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}[/tex]This way we eliminate the absolute value, because, remember, when x<0, |x| = -x
Related Questions
A wire is attached from the top of a 30-foot tall telephone pole…
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The diagram illustrating the given scenario is shown below
The triangle formed is a right triangle. From the diagram,
AB = height of pole
angle ACB is the angle between the and the pole
AC is the length of the wire
taking angle 48 as the reference angle,
hypotenuse = AC
adjacent side = BC = 30
θ = 48
We would find AC by applyng the Cosine trigonometric ratio which is expressed as
Cosθ = adjacent side/hypotenuse
By substituting these values into the formua, we have
Cos 48 = 30/AC
By crossmultiplying, we have
AC Cos 48 = 30
By dividing both sides of the equation by Cos 65, we have
AC = 30/Cos48
AC = 44.8
The length of the wire is 44.8 feet
4. A number between 200 and 400 with 6 more tens than ones.
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Answer
Question 3
Largest number where the sum of the digits is 16 is 862
Question 4
The number between 200 band 400 with 6 more tens than ones is 382
Explanation
We can only use numbers from the digit bank to answer this questions.
Question 3
Largest number where the sum of the digits is 16 is 862
Question 4
A number between 200 and 400 with 6 more tens than ones.
Noting that the tens digit is the second digit from the right in a number and the ones digit is the first number from the right for any number.
So, we are asked to form a number whose second number from the right is 6 more than the first number from the right.
So, we can easily see that
The ones number has to be 2
The tens number has to be 8 (Since 8 is 6 more than 2)
Then, for the third and last number, since the number has to be between 200 and 400, the last number has to be 3.
So, the number between 200 band 400 with 6 more tens than ones is 382
Hope this Helps!!!
100_0.22 help me please
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Given the expression :
[tex]100-0.22[/tex]The answer will be as follows, add the decimal point and two zeros
[tex]100-0.22=100.00-0.22[/tex]See the following picture:
how do I create equal groups that represent the division fact 28÷4=7?
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So to make equal groups just create the number of groups (divisor, in this case: 4) and insert into that the number of the quotient( in this case: 7)
1) Let's make equal groups for that division since 7 added 4 times is equal to 28:
2) Since 7 x 4 is the same as adding 7 four times, we have above four groups with seven balls that added up yields 28, in each group we have 7 balls.
3) So to make equal groups just create the number of groups (divisor) and insert into that the number of the quotient. Note that this is valid just for exact divisions.
An online auction company charges sellers a commission fee of 5.25% of an items final selling price. If you sell an item for 55$ what fee will you pay to the auction company ?
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The selling price of the item is $55.
The money charged by the auction company is;
[tex]\begin{gathered} 5.25\text{ \% of \$55} \\ \frac{5.25}{100}\times55 \\ =\text{ \$2.89} \end{gathered}[/tex]The fee paid to the auction company is $2.89
=In AABC, the measure of ZC=90°, CB = 35, AC = 12, and BArepresents the cosine of ZA?37. What ratio
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ANSWER:
[tex]\frac{12}{37}[/tex]STEP-BY-STEP EXPLANATION:
The first thing is to draw the triangle ABC:
We have that the trigonometric cosine ratio is given as follows
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{For A, we have} \\ \text{adjacent = 12} \\ \text{hypotenuse = }37 \\ \text{replacing:} \\ \cos A=\frac{12}{37} \end{gathered}[/tex]What is the component form of the vector represented by 8a when a=(-4,2)
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Given the vector represented by:
[tex]8a[/tex]You know that:
[tex]a\langle-4,2\rangle[/tex]By definition, the Component Form of a vector is:
[tex]\vec{V}=\langle x,y\rangle[/tex]In this case, you only need to multiply the coordinates of "a" by 8, in order to find the Component Form of:
[tex]8a[/tex]Therefore, you get:
[tex]=\langle(8)(-4),(8)(2)\rangle=\langle-32,16\rangle[/tex]Hence, the answer is:
[tex]\langle-32,16\rangle[/tex]hi, I would like help with this please and ty
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You can use number line or inequalities to compare the temperatures of this three different cities.
Using number line to compare the temperatures 2.5, -3.5 F and -5 F
Using inequality
[tex]\begin{gathered} 2.5>-3.5 \\ -3.5>-5 \end{gathered}[/tex]Help find the slope of the lined graph
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The slope of the line graph is -1.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Using (3, -3) and (-2, 2)
Therefore,
x₁ = 3
x₂ = - 2
y₁ = -3
y₂ = 2
Hence,
slope = 2 + 3 / -2 - 3
slope = 5 / -5
Therefore,
slope = - 1
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Divide the stars into 3 equal groups. How many stars are in each group? 8 What is 13 of 9?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total stars = 9
equal groups = 3
stars per group = ?
1/3 of 9 = ?
Step 02:
stars per group = total stars / equal groups
stars per group = 9 / 3
stars per group = 3
1/3 of 9 = 1/3 * 9 = 9/3 = 3
The answer:
There are 3 stars per group.
1/3 of 9 is 3.
The probability of picking an odd prime number is . The probability of picking a number greater than 0 that is also a perfect square is
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we know that
total blocks=10
total odd prime numbers------> 3,5,7------> 3 numbers
so
Part 1
The probability of picking an odd prime number is
P=3/10 or P=0.3Part 2
total blocks=10
total numbers greater than zero also a perfect square ------>1,4,9---> 3 numbers
so
The probability is
P=3/10 or P=0.3determine the ratio of surface area to volume of the triangular prism
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Solution
The surface area of a Triangular prism is given as;
[tex]SA=bh+(s_1+s_2+s_3)H[/tex]The volume of a triangular prism is given as;
[tex]V=\frac{1}{2}bhl[/tex]The ratio of surface area to volume of the triangular prism
[tex]\text{ratio}=\frac{SA}{V}=\frac{bh+(s_1+s_2+s_3)H}{\frac{1}{2}bhl}[/tex]A time traveler can take 4 books with him, and he has 86 books to choose from. How many differentways can the books be selected?
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Combination:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]n is the number of things to choose from, and r is the number of thing
explain the meaning of the point (1, 1 .5) in terms of the situation
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The graph above is a relationship between the amount of oil and the amount of vinegar use to prepare salad dressing. The point 1 is the x axis while the point 1.5 is the y axis .
In terms of the situation if the x axis represents the amount of oil required for the salad dressing and the y axis represents the amount of vinegar , the point (1, 1.5) says for every 1 table spoon of oil required , 1.5 table spoon of vinegar is also used to make the salad dressing.
Can you help me understand the steps to number 21 I think I got it wrong
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The probability of an event is determined a follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]We shall begin with the probability of selecting an even number as shown below;
[tex]\begin{gathered} P\lbrack\text{even\rbrack}=\frac{6}{12} \\ P\lbrack\text{even\rbrack}=\frac{1}{2} \end{gathered}[/tex]Next we shall calculate the probability of selecting a number less than 5 as shown below;
[tex]\begin{gathered} P\lbrack\text{less than 5\rbrack=}\frac{4}{12} \\ P\lbrack\text{less than 5\rbrack=}\frac{1}{3} \end{gathered}[/tex]The probability of event A OR event B occuring is calculated a follows;
[tex]\begin{gathered} P\lbrack A\rbrack\text{ OR P\lbrack{}B\rbrack=P\lbrack{}A\rbrack+P\lbrack{}B\rbrack} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{1}{2}+\frac{1}{3} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{3+2}{6} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{5}{6} \end{gathered}[/tex]The probability of selecting an even number or a number less than 5 is therefore
[tex]\frac{5}{6}[/tex]The correct answer is option A
What is 3 times 5????
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For natural numbers, a multiplication can be seen as a repetitive addition. In this case, 3 times 5 is the same as addign 5+5+5. Then:
[tex]3\times5=5+5+5=15[/tex]How would I create a logic proof for this question?
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Let us represent the premises given:
[tex]\begin{gathered} \text{Let } \\ A=\text{John is aardvark} \\ C=\text{Charles has a blue eye} \\ B=\text{Bob counts} \\ E=\text{Edna drives a truck} \\ D=\text{Dan edits} \end{gathered}[/tex]Then
We can subdivide the argument into substatement
Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts
[tex]A\Rightarrow(C\lor B)[/tex]Statement 2: If Charlene has a blue eye then Edna drives a truck
[tex]C\Rightarrow E[/tex]Statement 3: Either John is an aadvark or Dan edits
[tex]A\lor D[/tex]Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong
[tex]\begin{gathered} (B\lor E),\text{ But} \\ \sim(B\lor E) \end{gathered}[/tex]Therefor D
[tex]\therefore D[/tex]The above hypothesis and conclusion can be summarized below as;
Using a truth table calculator, the validity of the above arguments is shown below
Hence, we can conclude that the above is a valid argument.
a. a grade that is 12 points lower than a grade of x can be represented as Options: x-12both x-12 and 12-x 12-x
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a. If a friend says his grade is 12 points lower than your grade, it means your grade is greater than his grade, if your grade is represented by x, then the grade of your friend can be found by subtracting 12 from your grade, this can be written as:
[tex]x-12[/tex]b. If x represents your friend's grade instead of yours, then to find your grade you need to add 12 to his grade, it can be represented as:
[tex]\begin{gathered} x+12 \\ 12+x \end{gathered}[/tex]The correct answers are B. and D.
Can you please figure out this equation and see if I have the right answer
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The expression is given to be:
[tex]\tan \left(\frac{7\pi }{12}\right)[/tex]Rewrite the expression:
[tex]\frac{7\pi}{12}=\frac{\pi}{4}+\frac{\pi}{3}[/tex]Therefore, we have:
[tex]\tan\left(\frac{7\pi}{12}\right)=\tan\left(\frac{\pi}{4}+\frac{\pi}{3}\right)[/tex]Recall the summation identity:
[tex]\tan \left(x+y\right)=\frac{\tan \left(x\right)+\tan \left(y\right)}{1-\tan \left(x\right)\tan \left(y\right)}[/tex]Therefore, we have:
[tex]\tan\left(\frac{\pi}{4}+\frac{\pi}{3}\right)=\frac{\tan\left(\frac{\pi}{4}\right)+\tan\left(\frac{\pi}{3}\right)}{1-\tan\left(\frac{\pi}{4}\right)\tan\left(\frac{\pi}{3}\right)}[/tex]Recall that:
[tex]\begin{gathered} \tan \left(\frac{\pi }{4}\right)=1 \\ \tan \left(\frac{\pi }{3}\right)=\sqrt{3} \end{gathered}[/tex]Hence, the equation becomes:
[tex]\frac{\tan(\frac{\pi}{4})+\tan(\frac{\pi}{3})}{1-\tan(\pi\/4)\tan(\pi\/3)}=\frac{1+\sqrt{3}}{1-1\cdot\sqrt{3}}[/tex]Therefore, we can simplify the expression to be:
[tex]-2-\sqrt{3}[/tex]The THIRD OPTION is correct.
Find the radius when the arc is / and / radians
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The arc length formula is :
[tex]l=r\theta[/tex]where r = radius
θ = angle in radians
and l = arc length
From the problem, the arc length is 18π/7 and the angle is 6π/7.
Using the formula above :
[tex]\begin{gathered} \frac{18\pi}{7}=r(\frac{6\pi}{7}) \\ 18\pi=r(6\pi) \\ r=\frac{18\pi}{6\pi} \\ r=3 \end{gathered}[/tex]ANSWER :
The radius is 3
Can you just help me with this it is hurt
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A horizontal line is in the form
y =
This means the x component changes and the y component stays the same
( -7, 10)
The line is in the form
y = 10
x can be any value
The slope is zero since it is horizontal
The point ( 3,10) is on the line
The equation of the line is y = 10
The y intercept is 10 not -7
A rectangle or televisions length is 3 inches more than twice its width the perimeter of the television is 144 inches what is the width of the television
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The width of the television is 23 in.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
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i need help doing number 34 and 35 if you can please :(
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The tangent of an angle, we will follow the steps below
Step 1: Write out the trigonometric ratio to obtain the tangent of an angle
[tex]\tan \emptyset=\frac{opposite}{adjacent}[/tex]From question 35
Step 2: Apply the tangent ratio
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{60}{100}=\frac{6}{10}=\frac{3}{5} \\ \tan A=\frac{3}{5}=0.6000 \end{gathered}[/tex]For tan B
[tex]\begin{gathered} \tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{100}{60}=\frac{5}{3} \\ \tan B=\frac{5}{3}=1.6667 \end{gathered}[/tex]As shown above a classical deck of card is made up 52 cards suppose one card is selected at random and calculate the following proper ability
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To determine the probability of selecting a classical deck of card
(a) Probability of selecting a 7 or club
[tex]\begin{gathered} Pr(\text{selecting a 7 or club) = pr( selecting a 7) + pr(selecting a club )} \\ \text{pr( selecting a 7) = }\frac{4}{52} \\ \text{pr( selecting a club) = }\frac{13}{52} \\ Pr(\text{selecting a 7 or club) = }\frac{4}{52}+\frac{13}{52}=\text{ }\frac{4+13}{52}=\frac{17}{52}\text{ = 0.3269} \\ Pr(\text{selecting a 7 or club) = }0.327\text{ (3dp)} \end{gathered}[/tex](b) Probability of selecting a face card or heart
[tex]\begin{gathered} Pr(\text{selecting a face card or heart) = pr(selecting a face card) + pr(selecting a heart)} \\ Pr(\text{selecting a face card) = }\frac{12}{52} \\ Pr(\text{selecting a heart) = }\frac{13}{52} \\ Pr(\text{selecting a face card or heart) = }\frac{12}{52}+\frac{13}{52}=\frac{12+13}{52}=\frac{25}{52}=0.4807 \\ Pr(\text{selecting a face card or heart) }=\text{ 0.481 (3dp)} \end{gathered}[/tex](c) Probability of selecting both a face card and a club
[tex]\begin{gathered} Pr(\text{selecting both a face card and a club) = pr(selecting a face card)+pr(selecting a club)} \\ \text{pr(selecting a face card) = }\frac{12}{52} \\ \text{pr(selecting a club) = }\frac{13}{52} \\ Pr(\text{selecting both a face card and a club) = }\frac{12}{52}\text{ }\times\frac{13}{52}=\text{ }\frac{3}{52}=0.0577 \\ Pr(\text{selecting both a face card and a club) = 0.058 (3dp)} \end{gathered}[/tex]
Supposed to go out to a dinner and you spend $42 you want to leave a 20% tip how much money should you leave for a tip round your answer to the nearest cent
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Answer:
$8.4
Explanation:
To find how much money you should leave for a tip, we need to find how much is 20% of $42. So, to calculate this, we need to multiply 42 by 20 and then divide by 100, so:
$42 x 20% = 42 x 20 / 100 = 840 / 100 = 8.4
Therefore, the answer is $8.4
Enter the missing values in the area model to find 2(5n+1)
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First box: 10n
2
10n + 2
Explanations:The area model = 2 (5n + 1)
Thsi can expanded into:
2 (5n) and 2(1)
In the first box:
2 (5n) = 10n
In the second box:
2(1) = 2
In the third box:
2 (5n + 1) = 10n + 2
Given BD bisects ∠ABC, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.
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In order to prove that the triangles are congruent, we can write the following statements and reasons:
first box in the first row:
statement: BD bisects angle ABC
reason: given
first box in the second row:
statement: angle ABD congruent to angle DBC
reason: A segment bisector divides a segment into two congruent segments.
second box in the second row:
statement: angle ADB congruent to angle BDC
reason: given
third box in the second row:
statement: side AB congruent to side BC
reason: given
Since we have two pairs of congruent angles and one pair of congruent sides that are not between the angles, we can prove the triangles congruent by case AAS.
sue writes three different numbers. the numbers are all between 30 and 60 . the numbers all have 6 ones . what numbers does sue write
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EXPLANATION
The three numbers are 36, 46 and 56. This is because the only three numbers that have 6 ones and wich are included between 30 and 60 are 36, 46 and 56, no other number can comply that condition.
I need help on this
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You consider each parittion of the axis represents 1 unit.
You can notice that in the given image, the coordinates of the points A, B, C and D are the following:
A(-6,4)
B(-2,1)
C(2,3)
D(-1,-4)
where you have taken into account that point left side of the origin have negative x valuesand points right side have positive x values. Point down side of origin have negative y values and points above origin has positive y values.
72. Suppose that Sarah walks along a hiking trail at 2 mi/hra. What is her rate in mi/day?b. How many days will it take for her to reach a destination that is 14 1/2 miles away?c. If she started hiking at 6:00 am, what time will she reach her destination?
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Supposing the rate is:
[tex]2\frac{mi}{hour}[/tex](a) Converting tho mi/day
Knowing that 1 day = 24 hours
[tex]\begin{gathered} 2\text{ }\frac{mi}{hour}*\frac{24hour}{day} \\ 2*24\text{ }\frac{mi}{day} \\ 48\frac{m\imaginaryI}{day} \end{gathered}[/tex]The rate is 48 mi/day.
(b) Finding how many days will it take to reach 14 1/2
14 1/2 is the same as 14.5
Dividing 14.5 by 48:
[tex]\frac{14.5miles}{48\frac{miles}{day}}=0.3days[/tex]It will take 0.30 days.
(c) Finding when it will reach the destination.
Knowing the rate is 2 mi/hour, let's find how many hours it will take to reach 14.5 miles.
[tex]\begin{gathered} \frac{14.5mi}{2\text{ }\frac{mi}{hour}} \\ 7.25hours \end{gathered}[/tex]7.25 hours is 7 hours + 1/4 hour (15 min)
So, let's sum 06 (starting time) + 07 hours + 15 min
01:15 pm.
He will reach her destination at 01:15 pm.
Answer:
- (a) The rate is 48 mi/day.
- (b) It will take 0.30 days.
- (c) He will reach her destination at 01:15 pm.