Deck 13: Limits: a Preview of Calculus

Question 1

Use a table of values to estimate the value of . Use a graphing device to confirm your answer graphically.

Answer 1

It appears that .

Question 2

Evaluate , and justify each step by indicating the appropriate Limit Law(s).

Answer 2

Question 3

Evaluate the limit if it exists.

Answer 3

Question 4

Evaluate .

Question 5

For the function g whose graph is given, state the value of the given quantity if it exists.
a)
b)
c)

Question 6

Evaluate .

Question 7

Evaluate , and justify each step by indicating the appropriate Limit Law(s).

Question 8

For the function g whose graph is given, state the value of the given quantity if it exists.
a)
b)
c)

Question 9

For the function whose graph is given, state the value of the given quantity.

A)
B)
C)
D)

Question 10

Use a graphing device to determine whether exists. If the limit exists, estimate its value to two decimal places.

Question 11

Complete the table of values (to five decimal places) and use the table to estimate the value of .

Question 12

Evaluate the limit if it exists.

Question 13

Evaluate .

Question 14

Evaluate .

Question 15

Evaluate the limit if it exists.

Question 16

Evaluate .

Question 17

Use a table of values to estimate the value of . Use a graphing device to confirm your answer.

Question 18

For the function g whose graph is given, state the value of the given quantity if it exists.

a)
b)

Question 19

Use a table of values to estimate the value of . Use a graphing device to confirm your answer graphically.

Question 20

Evaluate the limit if it exists.

Question 21

Find the value of , if it exists. If the limit does not exist, explain why.

Question 22

Find the derivative of the function at the given number. at 4

Question 23

Find the derivative of the function at the given number. at 2

Question 24

Find the derivative of at the point .

Question 25

Find the derivative of the function at the given number. at 4

Question 26

Find , where a is in the domain of f.

Question 27

Find the slope of the tangent line of the graph of at the point .

Question 28

Find the derivative of at the point .

Question 29

If , find .

Question 30

Find the slope of the tangent line of the graph of at the point .

Question 31

Find the value of , if it exists. If the limit does not exist, explain why.

Question 32

If , find .

Question 33

Find the derivative of the function at the given number. at 1

Question 34

Find the equation of the tangent line to the curve at the point .

Question 35

Find the equation of the tangent line to the curve at the point .

Question 36

Find the derivative of the function at the given number. at 1

Question 37

Find the value of , if it exists. If the limit does not exist, explain why.

Question 38

Find the derivative of the function at the given number. at 2

Question 39

Find the slope of the tangent line of the graph of at the point .

Question 40

Find the derivative of at the point .

Question 41

Estimate the area under the graph of from to using
(a) four approximating rectangles and right endpoints.
(b) four approximating rectangles and left endpoints.
(c) eight approximating rectangles and right endpoints.

Question 42

Use a table of values to estimate the value of . Then use a graphing device to confirm your result graphically.

Question 43

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 44

Find .

Question 45

Use a table of values to estimate the value of . Then use a graphing device to confirm your result graphically.

Question 46

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 47

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 48

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 49

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 50

A particle moves in a straight line with its displacement of motion described by equation , where is measured in feet and is measured in seconds. Find the velocity of at , , , and .

Question 51

Find .

Question 52

Find .

Question 53

Use a table of values to estimate the value of . Then use a graphing device to confirm your result graphically.

Question 54

Estimate the area under the graph of from to using
(a) four approximating rectangles and right endpoints.
(b) four approximating rectangles and left endpoints.
(c) eight approximating rectangles and right endpoints.

Question 55

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 56

Estimate the area under the graph of from to using
(a) four approximating rectangles and right endpoints.
(b) four approximating rectangles and left endpoints.
(c) eight approximating rectangles and right endpoints.

Question 57

Use a table of values to estimate the value of . Then use a graphing device to confirm your result graphically.

Question 58

Determine whether the sequence converges or diverges. If it converges, find the limit.

Question 59

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 60

A stone is dropped into a pond causing a circular ripple in the water. Find the rate of change of the area of the circle with respect to the radius when ft.

Question 61

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 62

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 63

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 64

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 65

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .

Question 66

Use the definition of area as a limit to find the area of the region that lies under the graph of over the interval .