Question 1

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

Accepted Answer

A)  -64 
B)    
C)    
D)    
A)  -64 
B)    
C)    
D)

Question 2

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.

Accepted Answer

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

Question 3

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.

Accepted Answer

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

Question 4

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$.

Accepted Answer

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

Question 5

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

Accepted Answer

A)  3 
B)    
C)    
D)    
A)  3 
B)    
C)    
D)

Question 6

Evaluate the limit using the limit properties.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Evaluate the limit using the limit properties.

Accepted Answer

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

Question 9

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

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 10

Evaluate the following limit.

Accepted Answer

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

Question 11

Evaluate the limit.

Accepted Answer

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

Question 12

Evaluate the limit by rewriting the given expression as needed.

Accepted Answer

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

Question 13

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

Accepted Answer

A)    
B)    
C)    
D)  0 
A)    
B)    
C)    
D)  0

Question 14

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.

Accepted Answer

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

Question 15

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

Accepted Answer

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.
  
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 16

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

Accepted Answer

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

Question 17

Evaluate the limit by rewriting the given expression as needed.

Accepted Answer

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

Question 18

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.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

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.

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

Evaluate the limit using the limit properties.

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

Evaluate the limit using the limit properties.

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

Evaluate the following limit.

Evaluate the limit.

Evaluate the limit by rewriting the given expression as needed.

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

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

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

Evaluate the limit by rewriting the given expression as needed.

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.

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

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

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Review of Basic Concepts and Skills

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Exam 11: Bridges to Calculus - an Introduction to Limits

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

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.

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

Evaluate the limit using the limit properties.

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

Evaluate the limit using the limit properties.

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

Evaluate the following limit.

Evaluate the limit.

Evaluate the limit by rewriting the given expression as needed.

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

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

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

Evaluate the limit by rewriting the given expression as needed.

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.

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

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

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Review of Basic Concepts and Skills

Filters