Question 1

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

As $ x $ approaches 0, $ x^2 $ approaches 0 and $\cos x$ approaches 1, so the limit of the fraction is 0.

Question 2

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

B

Question 3

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

To find the limit as $x$ approaches 2 for the function $x^2 + 8x - 2$, substitute $x = 2$ into the function: $2^2 + 8(2) - 2 = 4 + 16 - 2 = 18$. This calculation shows that the limit is 18.

Question 4

Use the graph shown to determine if the limit exists. If it does, find its value.&#10; &#10;A) 1&#10;B) -1&#10;C) 4&#10;D) does not exist

Accepted Answer

The answer of Use the graph shown to determine if...

Question 5

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

The expression $\frac { d ^ { 3 } - 27 } { d - 3 }$ can be simplified using the difference of cubes formula, $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, to $\frac { (d - 3)(d^2 + 3d + 9) } { d - 3 }$. When $d \neq 3$, the $d - 3$ terms cancel out, leaving $d^2 + 3d + 9$. Substituting $d = 3$ into this simplified expression gives $3^2 + 3(3) + 9 = 9 + 9 + 9 = 27$. However, the original question asks for the limit as $d$ approaches 3, not the value of the expression at $d = 3$. The correct approach is to evaluate the derivative of the numerator at $d = 3$, which gives $3(3)^2 = 27$, indicating a slope or rate of change at that point, but this explanation mistakenly calculates the value after canceling out the terms. The correct calculation for the limit involves recognizing that after cancelation, we directly substitute $d = 3$ into the simplified form $d^2 + 3d + 9$, which was incorrectly described in the explanation. The correct substitution should be directly into the derivative if we were following that method, or more accurately, into the simplified form before taking any derivative. The actual limit calculation involves evaluating the simplified expression at $d = 3$, which is $3^2 + 3*3 + 9 = 9 + 9 + 9 = 27$, but this is not the limit; it's the value after simplification and incorrect for the limit context. The correct process is to recognize that after simplification, the limit as $d$ approaches 3 of $d^2 + 3d + 9$ is indeed evaluated directly by substituting $d = 3$, leading to $3^2 + 3*3 + 9$, which simplifies to $9 + 9 + 9$, but the actual limit sought is the coefficient of $d$ in the linear term of the simplified expression, which is $3$, times 3, giving a correct limit of $27$, which is a misinterpretation of the process. The correct limit as $d$ approaches 3 is found by directly evaluating the simplified expression at $d = 3$, which is $9 + 9 + 9 = 27$, but this is a misinterpretation. The actual limit, correctly calculated, is $27$, but due to a mistake in the explanation process. The correct answer, based on the simplification and direct substitution into $d^2 + 3d + 9$, is $27$, which corresponds to a mistake in the explanation provided. The correct limit as $d$ approaches 3, without any mistakes in the explanation, is found by evaluating the simplified expression $d^2 + 3d + 9$ at $d = 3$, which indeed gives $27$, but this explanation mistakenly conflates the process of finding the limit with evaluating the expression at $d = 3$ and incorrectly describes the mathematical process involved. The correct answer, without any errors in explanation, is that the limit as $d$ approaches 3 of the given expression is $27$, which is a result of simplifying the expression and directly substituting $d = 3$ into the simplified form, not from evaluating the derivative or incorrectly calculating the value after simplification. The correct explanation for finding the limit involves recognizing the cancellation of the $d - 3$ term and directly substituting $d = 3$ into the remaining expression, leading to the correct limit of $27$, which is not due to the derivative or a misinterpretation of the process.

Question 6

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

As $x$ approaches 0, the expression $\frac{x + 2}{5x + 2}$ simplifies to $\frac{2}{2} = 1$. Thus, the limit is 1.

Question 7

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) 1&#10;B) -2&#10;C) -8&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 8

Use the graph shown to determine if the limit exists. If it does, find its value.&#10;

Accepted Answer

The answer of Use the graph shown to determine if...

Question 9

Find the limit algebraically.&#10;

Accepted Answer

The limit of a constant as x approaches any value is simply the constant itself, so the limit is -6.

Question 10

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) -2&#10;B) -6&#10;C) -8&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 11

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 12

Use the graph shown to determine if the limit exists. If it does, find its value.&#10; &#10;A) 0&#10;B) 1&#10;C) 2&#10;D) does not exist

Accepted Answer

The answer of Use the graph shown to determine if...

Question 13

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) -1&#10;B) 3&#10;C) -2&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 14

Use the TABLE feature of a graphing utility to find the limit.&#10;

Accepted Answer

The answer of Use the TABLE feature of a graphing...

Question 15

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) 12&#10;B) 11&#10;C) 2&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 16

Use the graph shown to determine if the limit exists. If it does, find its value.&#10; &#10;A) 4&#10;B) 3&#10;C) 5&#10;D) does not exist

Accepted Answer

The answer of Use the graph shown to determine if...

Question 17

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) 0&#10;B) 1&#10;C) 5&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 18

Use the grid to graph the function. Find the limit, if it exists&#10; &#10;A) -5&#10;B) 1&#10;C) 5&#10;D) does not exist

Accepted Answer

The answer of Use the grid to graph the function....

Question 19

Use a graphing utility to find the indicated limit rounded to two decimal places.&#10;

Accepted Answer

The answer of Use a graphing utility to find the...

Question 20

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 21

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 22

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 23

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 24

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 25

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 26

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 27

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 28

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 29

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 30

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 31

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 32

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 33

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 34

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 35

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 36

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 37

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 38

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 39

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 40

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 41

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 42

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 43

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 44

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 45

Find the one-sided limit.&#10;

Accepted Answer

The answer of Find the one-sided limit.&#10; ...

Question 46

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 47

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 48

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 49

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 50

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 51

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 52

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 53

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 54

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 55

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 56

Find the limit algebraically.&#10;

Accepted Answer

The answer of Find the limit algebraically.&#10; ...

Question 57

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 58

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 59

Find the limit as x approaches c of the average rate of change of the function from c to x.&#10;

Accepted Answer

The answer of Find the limit as x approaches c...

Question 60

Use the graph of y = g(x) to answer the question.  &#10;

Accepted Answer

The answer of Use the graph of y = g(x)...

Question 61

Determine whether f is continuous at c.&#10;

Accepted Answer

The answer of Determine whether f is continuous at c.&#10;...

Question 62

Find the one-sided limit.&#10;

Accepted Answer

The answer of Find the one-sided limit.&#10; ...

Question 63

Find the one-sided limit.&#10;

Accepted Answer

The answer of Find the one-sided limit.&#10; ...

Question 64

Determine whether f is continuous at c.&#10;

Accepted Answer

The answer of Determine whether f is continuous at c.&#10;...

Deck 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function