Deck 11: Bridges to Calculus - an Introduction to Limits

Question 1

Evaluate the limits using limit properties. If a limit does not exist, state why.

A)
B)
C)
D)

Answer 1

Question 2

Evaluate the limits using limit properties. If a limit does not exist, state why.

A) 3
B)
C)
D)

Answer 2

Question 3

Evaluate the limits using limit properties. If a limit does not exist, state why.

A) -64
B)
C)
D)

Answer 3

Question 4

Evaluate the limit using the limit properties.

A)
B)
C)
D)

Question 5

The function g (x) has a hole (discontinuity) in its graph at x = 6. Write a related piecewise-defined function that creates a continuous graph.

A) G (x)
B) G (x)
C) G (x)
D) G (x)

Question 6

Use a table of values to evaluate the function as x approaches the value indicated. If the function seems to approach a limiting value, write the relationship using limit notation. ; x $\rarr$ 0

A)
B)
C)
D) no limiting value

Question 7

Evaluate the limit using the limit properties.

A) -93
B) 93
C) -21
D) 21

Question 8

Evaluate the limit using a table of values. Given , find .

A)
B)
C). $\infty$
D). - $\infty$

Question 9

Evaluate the limit using a table of values. Given , find .

A)
B)
C)
D) 0

Question 10

Evaluate the limit using the limit properties.

A)
B)
C)
D)

Question 11

Evaluate the limit using a table of values. Given , find .

A) 2
B) -2
C) 4
D) -4

Question 12

Evaluate the limits using a table of values. Given , find:
I. ii. iii.

A) i. -4 ii. -4
Iii. -4
B) i. 4 ii. 4
Iii. 4
C) i. 4 ii. -4
Iii.

D) i. -4 ii. 4
Iii.

Question 13

Evaluate the limits using a table of values. Given , find:
I. ii. iii.

A) i. 13 ii. 13
Iii. 13
B) i. 46 ii. 46
Iii. 46
C) i. 13 ii. 46
Iii.

D) i. 46 ii. 13
Iii.

Question 14

Evaluate the limits using a table of values. Given , find:
I. ii. iii.

A) i. -1 ii. -1
Iii. -1
B) i. 1 ii. 1
Iii. 1
C) i. 1 ii. -1
Iii.

D) i. -1 ii. 1
Iii.

Question 15

Evaluate the limit using the limit properties.

A) -1331
B) 1331
C) 343
D) -343

Question 16

Evaluate the limit using the limit properties.

A) 0
B) -6
C) -12
D) 12

Question 17

Evaluate the limits using a table of values. Given , find:
I. ii.

A) i. 4 ii. 0
B) i. -2 ii. 0
C) i. 0 ii. 4
D) i. 0 ii. 0

Question 18

See if a table of values suggests a limit for the function and approach indicated. as x $\rarr$ 4 from the right

A) 0
B) 1
C) -1
D) no limiting value

Question 19

Evaluate the limit using the limit properties.

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

Question 20

Evaluate the limit using the limit properties.

A) -8
B) 4
C) 12
D) -4

Question 21

Find the area under the curve for the function and interval given, using the rectangle method and n subintervals of equal width. ,

A) units²
B) units²
C) units²
D) units²

Question 22

For a new machine shop employee, the rate of production for a specialized part is modeled by the function (production increases quickly with experience), where represents the number of parts completed per day. The area under this curve in the interval represents the total number of parts produced in the first two days. Using the rectangle method results in the expression . Find the number of parts produced by applying the summation properties/formulas and taking the limit as n $\rarr$$\infty$ .

A) 11 parts
B) 9 parts
C) 7 parts
D) 5 parts

Question 23

Use a table of values to evaluate the following limit at positive infinity.

A) 0
B)
C)
D)

Question 24

Evaluate the limit by rewriting the given expression as needed.

A)
B)
C) 0
D) 1

Question 25

Find the limit of the difference quotient of the given function f (x) to obtain a function that represents the slope of a line drawn tangent to the curve at x. Use the results to find the slope of the line tangent to the graph of f (x) at x = -3.

A) ;

B) ;

C) ;

D) ;

Question 26

The population of a small town can be modeled by the function , where p is measured in thousands and t is the number of years after 2008. Find the limit of the difference quotient for p, to obtain a function that represents the instantaneous rate of change of population at time t. Use the results to find the instantaneous rate of change of the population of the town in 2024 to the nearest person/yr.

A) ; 25600 people/yr
B) ; 6400 people/yr
C) ; 200 people/yr
D) ; 50 people/yr

Question 27

A window washer's bucket falls off a scaffold 248 feet above the street. Its height in feet, t seconds after it falls, can be modeled by . Find the limit of the difference quotient for d, to obtain a function that represents the instantaneous velocity of the bucket at time t. Use the results to find the instantaneous velocity of the bucket at t = 3.

A) ; -344 ft/sec
B) ; 152 ft/sec
C) ; -112 ft/sec
D) ; -96 ft/sec

Question 28

Use a table of values to evaluate the following limit at negative infinity.

A) 0
B)
C)
D)

Question 29

Find the limit of the difference quotient for the function f (x) given, to obtain a function that represents the instantaneous rate of change at x for the function.

A)
B)
C)
D)

Question 30

Find the limit of the difference quotient for the function f (x) given, to obtain a function that represents the instantaneous rate of change at x for the function.

A)
B)
C)
D)

Question 31

Evaluate the limit by dividing the numerator and denominator by the highest power of x occurring in the denominator.

A) 0
B)
C)
D)

Question 32

Use the graphs of f and g to evaluate the limits necessary to complete the calculation. If the computation is not possible, state why. f (x) g (x)

A) not possible, does not exist
B) not possible, does not exist
C) 0
D) 4

Question 33

Use a table of values to evaluate the following limit at negative infinity.

A) 0
B) 1
C) -1
D)

Question 34

Evaluate the limit.

A) 0
B) 2
C). -2
D)

Question 35

Find the limit of the difference quotient for the function f (x) given, to obtain a function that represents the instantaneous rate of change at x for the function.

A)
B)
C)
D)

Question 36

Evaluate the limit by rewriting the given expression as needed.

A) 5
B) -5
C) 0
D) 1

Question 37

Evaluate the limit by using direct substitution, if possible. If not possible, state why.

A) 5
B) -5
C) 43
D) direct substitution not possible, 3 is not in the domain

Question 38

Evaluate the limit by using direct substitution, if possible. If not possible, state why.

A)
B)
C)
D) direct substitution not possible, -4 is not in the domain

Question 39

Find the limit of the difference quotient for the function f (x) given, to obtain a function that represents the instantaneous rate of change at x for the function.

A)
B)
C)
D)

Question 40

Evaluate the following limit.

A) 36 units²
B) 12 units²
C) 18 units²
D) 6 units²