Question 1

Given that   and   , find, if it exists,   .

Accepted Answer

A)  -676 
B)  676 
C)  1 
D)  -26 
E)  It does not exist 
A)  -676 
B)  676 
C)  1 
D)  -26 
E)  It does not exist

Question 2

Find the limit.

Accepted Answer

A)  0 
B)  -1 
C)  1 
D)  +$\infty$ 
E)  -$\infty$ 
A)  0 
B)  -1 
C)  1 
D)  +$\infty$ 
E)  -$\infty$

Question 3

Find the limit.

Accepted Answer

A)  0 
B)    
C)    
D)  +$\infty$ 
E)  -$\infty$ 
A)  0 
B)    
C)    
D)  +$\infty$ 
E)  -$\infty$

Question 4

Find   .

Accepted Answer

The answer of Find   ....

Question 5

Find a least number  $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| <  $\delta$.   ; $\varepsilon$ = 0.005.

Accepted Answer

A)  0.002 
B)  0.004 
C)  0.005 
D)  0.007 
E)  0.008 
A)  0.002 
B)  0.004 
C)  0.005 
D)  0.007 
E)  0.008

Question 6

Let   . Then

Accepted Answer

The answer of Let   . Then  ...

Question 7

Find   .

Accepted Answer

The answer of Find   ....

Question 8

To prove that   , where   , a reasonable relationship between   $\delta$ and $\varepsilon$ would be

Accepted Answer

A)    $\delta$ = 4$\varepsilon$ 
B)    $\delta$ =   
C)    $\delta$ = 4$\varepsilon$ + 6 
D)    $\delta$ = 2$\varepsilon$ 
E)    
A)    $\delta$ = 4$\varepsilon$ 
B)    $\delta$ =   
C)    $\delta$ = 4$\varepsilon$ + 6 
D)    $\delta$ = 2$\varepsilon$ 
E)

Question 9

Find a least number $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| < $\delta$ .   ; $\varepsilon$ = 0.187

Accepted Answer

A)  1 
B)  0.187 
C)  0.017 
D)  0.014 
E)  0.021 
A)  1 
B)  0.187 
C)  0.017 
D)  0.014 
E)  0.021

Question 10

Determine if the discontinuity at x = 0 in the function   is removable.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& So the limit @#IMG-DLM& does

Question 11

Approximate the horizontal asymptote of   .

Accepted Answer

A)  -8 
B)  8 
C)  -11 
D)  2 
E)  11 
A)  -8 
B)  8 
C)  -11 
D)  2 
E)  11

Question 12

Define   so that it will be continuous everywhere.

Accepted Answer

The answer of Define   so that it will...

Question 13

Assign a value to the constant k which will make g continuous.

Accepted Answer

The answer of Assign a value to the constant k...

Question 14

Find   .

Accepted Answer

The answer of Find   ....

Question 15

Answer true or false. It is possible to prove that   .

Accepted Answer

A) True 
 B)False

Question 16

Find a least positive number N such that |f(x) - L|  N.   ; $\varepsilon$ = 0.05

Accepted Answer

A)  400 
B)  20 
C)  40 
D)  100 
E)  200 
A)  400 
B)  20 
C)  40 
D)  100 
E)  200

Question 17

Answer true or false. It can be shown that if |f(x) - L| 2 - 9| < $\varepsilon$ if |x - 3| <  $\delta$ for arbitrarily small positive $\varepsilon$.

Accepted Answer

A) True 
 B)False

Question 18

Find

Accepted Answer

The answer of Find  ...

Question 19

Answer true or false.

Accepted Answer

A) True 
 B)False

Question 20

Answer true or false. f(x) = x4 - 2x2 + 11 = 0 has at least one solution on the interval [0, 9].

Accepted Answer

A) True 
 B)False

Given that and , find, if it exists, .

Find the limit.

Find the limit.

Find .

Find a least number $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| < $\delta$ . $Find a least number \delta such that |f(x) - L| < \varepsilon if 0 < |x - a| < \delta . ; \varepsilon = 0.005.$ ; $\varepsilon$ = 0.005.

Let . Then

Find .

To prove that $To prove that , where , a reasonable relationship between \delta and \varepsilon would be$ , where $To prove that , where , a reasonable relationship between \delta and \varepsilon would be$ , a reasonable relationship between $\delta$ and $\varepsilon$ would be

Find a least number $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| < $\delta$ . $Find a least number \delta such that |f(x) - L| < \varepsilon if 0 < |x - a| < \delta . ; \varepsilon = 0.187$ ; $\varepsilon$ = 0.187

Determine if the discontinuity at x = 0 in the function is removable.

Approximate the horizontal asymptote of .

Define so that it will be continuous everywhere.

Assign a value to the constant k which will make g continuous.

Find .

Answer true or false. It is possible to prove that .

Find a least positive number N such that |f(x) - L| < $\varepsilon$ if x > N. $Find a least positive number N such that |f(x) - L| < \varepsilon if x > N. ; \varepsilon = 0.05$ ; $\varepsilon$ = 0.05

Answer true or false. It can be shown that if |f(x) - L| < $\varepsilon$ when 0 < |x - a| < $\delta$ , then |x² - 9| < $\varepsilon$ if |x - 3| < $\delta$ for arbitrarily small positive $\varepsilon$ .

Find

Answer true or false.

Answer true or false. f(x) = x⁴ - 2x² + 11 = 0 has at least one solution on the interval [0, 9].

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 1: Limits and Continuity

Given that and , find, if it exists, .

Find the limit.

Find the limit.

Find .

Find a least number δ\deltaδ such that |f(x) - L| < ε\varepsilonε if 0 < |x - a| < δ\deltaδ . ; ε\varepsilonε = 0.005.

Let . Then

Find .

To prove that , where , a reasonable relationship between δ\deltaδ and ε\varepsilonε would be

Find a least number δ\deltaδ such that |f(x) - L| < ε\varepsilonε if 0 < |x - a| < δ\deltaδ . ; ε\varepsilonε = 0.187

Determine if the discontinuity at x = 0 in the function is removable.

Approximate the horizontal asymptote of .

Define so that it will be continuous everywhere.

Assign a value to the constant k which will make g continuous.

Find .

Answer true or false. It is possible to prove that .

Find a least positive number N such that |f(x) - L| < ε\varepsilonε if x > N. ; ε\varepsilonε = 0.05

Answer true or false. It can be shown that if |f(x) - L| < ε\varepsilonε when 0 < |x - a| < δ\deltaδ , then |x2 - 9| < ε\varepsilonε if |x - 3| < δ\deltaδ for arbitrarily small positive ε\varepsilonε .

Find

Answer true or false.

Answer true or false. f(x) = x4 - 2x2 + 11 = 0 has at least one solution on the interval [0, 9].

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find a least number $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| < $\delta$ . $Find a least number \delta such that |f(x) - L| < \varepsilon if 0 < |x - a| < \delta . ; \varepsilon = 0.005.$ ; $\varepsilon$ = 0.005.

To prove that $To prove that , where , a reasonable relationship between \delta and \varepsilon would be$ , where $To prove that , where , a reasonable relationship between \delta and \varepsilon would be$ , a reasonable relationship between $\delta$ and $\varepsilon$ would be

Find a least number $\delta$ such that |f(x) - L| < $\varepsilon$ if 0 < |x - a| < $\delta$ . $Find a least number \delta such that |f(x) - L| < \varepsilon if 0 < |x - a| < \delta . ; \varepsilon = 0.187$ ; $\varepsilon$ = 0.187

Find a least positive number N such that |f(x) - L| < $\varepsilon$ if x > N. $Find a least positive number N such that |f(x) - L| < \varepsilon if x > N. ; \varepsilon = 0.05$ ; $\varepsilon$ = 0.05

Answer true or false. It can be shown that if |f(x) - L| < $\varepsilon$ when 0 < |x - a| < $\delta$ , then |x² - 9| < $\varepsilon$ if |x - 3| < $\delta$ for arbitrarily small positive $\varepsilon$ .

Answer true or false. f(x) = x⁴ - 2x² + 11 = 0 has at least one solution on the interval [0, 9].