Deck 11: Limits: A Preview to Calculus

Question 1

Evaluate the summation.

Answer 1

Question 2

Evaluate the summation.

Answer 2

Question 3

Evaluate the summation.

Answer 3

Question 4

Evaluate the summation.

Question 5

Evaluate the summation.

Question 6

Find the limit of the summation.

Question 7

Find the limit of the summation.

Question 8

Find the limit of the summation.

Question 9

Find the limit of the summation.

Question 10

Approximate the area under the curve (between the graph of f, the x-axis, x = 0 and x = 4) using the four rectangles of equal width and left endpoints.

Question 11

Approximate the area under the curve using the given number of rectangles of equal width.
on
; four rectangles with right endpoints

Question 12

Approximate the area under the curve using the given number of rectangles of equal width.
on
; four rectangles with rightendpoints

Question 13

Approximate the area under the curve using the given number of rectangles of equal width. Round your answer to 3 decimal places.
on
; eight rectangles with leftendpoints

Question 14

Approximate the area under the curve using the given number of rectangles of equal width.
on
; four rectangles with rightendpoints

Question 15

Find the area under the curve on the specified interval.

Question 16

Find the area under the curve on the specified interval.

Question 17

Find the area under the curve on the specified interval.

Question 18

Find the area under the curve on the specified interval.

Question 19

Find the area under the curve on the specified interval.

Question 20

Calculate the work exerted when a man pushes with a force of pounds from x = 0 to x = 5 feet.

Question 21

Approximate the area under the curve (between the graph of f, the x-axis, x = 0 and x = 2) using 4 rectangles and using left endpoints.

Question 22

Approximate the area under the curve (between the graph of f, the x-axis, x = 0 and x = 3) using 6 rectangles and using right endpoints.

Question 23

Find the limit, if it exists.

Question 24

Find the limit, if it exists.

Question 25

Find the limit, if it exists.

Question 26

Find the limit, if it exists.

Question 27

Find the limit, if it exists.

Question 28

Find the limit, if it exists.

Question 29

Find the limit, if it exists.

Question 30

Find the limit, if it exists.

Question 31

Determine whether the sequence converges. If it does converge, state the limit.

Question 32

Determine whether the sequence converges. If it does converge, state the limit.

Question 33

Determine whether the sequence converges. If it does converge, state the limit.

Question 34

Determine whether the sequence converges. If it does converge, state the limit.

Question 35

The concentration C of a particular drug (in mg/dL) in a person's bloodstream t minutes after injection is given by
. What do you expect the concentration to be after several days?

Question 36

Find the limit, if it exists.

A) 0
B) $\infty$
C) 6
D) -6

Question 37

Find the limit, if it exists.

A) $\infty$
B) - $\infty$
C) 0
D) -3/20

Question 38

Find the limit, if it exists.

A) -7/17
B) 0
C) $\infty$
D) 13/2

Question 39

Find the limit, if it exists.

A) - $\infty$
B) $\infty$
C) 0
D) -1/6

Question 40

Find the limit, if it exists.

A) -3
B) 0
C) - $\infty$
D) $\infty$

Question 41

Find the limit, if it exists.

A) Does not exist
B) 0
C) 1
D) -1

Question 42

Find the limit, if it exists.

A) -15/13
B) 5/16
C) 0
D) $\infty$

Question 43

Find the limit, if it exists.

A) 19
B) -17
C) - $\infty$
D) 0

Question 44

Determine whether the sequence converges. If it does converge, state the limit.

A)
B)
C) sequence diverges
D)

Question 45

Determine whether the sequence converges. If it does converge, state the limit.

A) 0
B) sequence diverges
C) 1/2
D) 1

Question 46

Determine whether the sequence converges. If it does converge, state the limit.

A)
B)
C) 3
D) sequence converges, 0

Question 47

Determine whether the sequence converges. If it does converge, state the limit.

A) 36
B) 0
C) 12
D) sequence diverges

Question 48

The concentration C of a particular drug in a person's bloodstream t minutes after injection is given by . What do you expect the concentration to be after several days?

A) 0
B) 4
C) 85
D) $\infty$

Question 49

Find the limit, if it exists.

Question 50

Find the limit, if it exists.

Question 51

Find the slope of the tangent line to the graph of f at the given point.
at the point

Question 52

Find the slope of the tangent line to the graph of f at the given point.
at the point

Question 53

Find the slope of the tangent line to the graph of f at the given point.
at the point

Question 54

Find the equation of the tangent line to the graph of f at the given point.
at the point

Question 55

Find the equation of the tangent line to the graph of f at the given point.
at the point

Question 56

Find the equation of the tangent line to the graph of f at the given point.
at the point

Question 57

Find the derivative of the function at the specified value of x.

Question 58

Find the derivative of the function at the specified value of x.

Question 59

Find the derivative of the function at the specified value of x.

Question 60

Find the derivative of the function at the specified value x.

Question 61

Find the derivative f '(x).

Question 62

Find the derivative of f '(x).

Question 63

Find the derivative of f '(x).

Question 64

Find the derivative of f '(x).

Question 65

Find the derivative of the f '(x).

Question 66

A person holds a pistol straight upward and fires. The initial velocity of most bullets is around 1,490 feet per second. The height of the bullet t seconds after it is fired is a function described by

a. What is the average of the bullet between 37 and 89 seconds after it is fired?
b. What is the instantaneous velocity of the bullet when t = 91 seconds (shortly before its hits the ground)?

Question 67

The gas mileage (miles per gallon, mpg) for a typical sedan can be approximated by the quadratic function

, where x represents the speed of the car in miles per hour (mph) and f represents the gas mileage in mpg. Find the instantaneous rate of change of the gas mileage of this sedan when the speed is 68 mph.

Question 68

If the profit function P(x) in dollars corresponding to producing x units is given by

. Find the instantaneous rate of change of the profit when x = 113 units. Is the profit increasing or decreasing at 113 units? What is the meaning of P '(x) and what are its units?

Question 69

Find the slope of the tangent line to the graph of f at the given point. at the point

A) 7
B) -12
C) 8
D) 1

Question 70

Find the slope of the tangent line to the graph of f at the given point. at the point

A)
B)
C)
D)

Question 71

Find the slope of the tangent line to the graph of f at the given point. at the point

A)
B)
C)
D)

Question 72

Find the equation of the tangent line to the graph of f at the given point. at the point

A)
B)
C)
D)

Question 73

Find the derivative of the function at the specified value of x.

A)
B)
C)
D)

Question 74

Find the derivative of the function at the specified value of x.

A)
B)
C)
D)

Question 75

Find the derivative of f '(x).

A)
B)
C)
D)

Question 76

Find the derivative of f '(x).

A)
B)
C)
D)

Question 77

Find the derivative of f '(x).

A)
B)
C)
D)

Question 78

Find the derivative of the f '(x).

A)
B)
C)
D)

Question 79

Given the graphs of the functions f and g, find the limit, if it exists.

Question 80

Given the graphs of the functions f and g, find the limit, if it exists.