Question 1

Find the values of x for which the function is continuous.

Accepted Answer

The answer of Find the values of x for which...

Question 2

Find the values of x for which the function is continuous.

Accepted Answer

The answer of Find the values of x for which...

Question 3

Use the graph of the function f to find  and  if the limit exists.

Accepted Answer

The answer of Use the graph of the function f...

Question 4

Determine all values of x at which the function is discontinuous.

Accepted Answer

The answer of Determine all values of x at which...

Question 5

Find  and  , where  .

Accepted Answer

The answer of Find  and  , where ...

Question 6

A function f is continuous at the point  if the following conditions are satisfied. 1.  is defined.
2)  exists.
3)  .
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Accepted Answer

The answer of A function f is continuous at the...

Question 7

Use the graph of the function f to find  and  if the limit exists.

Accepted Answer

The answer of Use the graph of the function f...

Question 8

A function f is continuous at the point  if the following conditions are satisfied. 1.  is defined.
2)  exists.
3)  .
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Accepted Answer

At point C, the function is discontinuous because condition 3 is violated. The limit as x approaches C exists, but is not equal to f(C). Therefore, condition 3 (the limit of the function as x approaches the point must be equal to the value of the function at the point) is violated. 
At all other points, the function satisfies all three conditions for continuity, so it is continuous everywhere except at point C.

Question 9

Find the one-sided limit, if it exists.

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 10

Find  and  , where

Accepted Answer

The answer of Find  and  , where 
...

Question 11

The base salary of a salesman working on commission is $13,000. For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Accepted Answer

The answer of The base salary of a salesman working...

Question 12

Find the indicated one-sided limit.

Accepted Answer

Without the actual function, it is impossible to determine the exact limit value. However, the fact that the expression in the limit is changing from `0274` to `2985` to `2986` suggests that the limit is approaching a specific value, rather than approaching positive or negative infinity. Therefore, choices A, B, and C can be eliminated. Between choices D and E, the change from `2985` to `2986` is a small increment, indicating that D may be the better choice as it suggests a limit that approaches a specific value.

Question 13

Let  . Find the zeros of f in  by solving the equation  .

Accepted Answer

The answer of Let  . Find the zeros of...

Question 14

Refer to the graph of the function f and determine whether the statement below is true or false.

Accepted Answer

The graph of the function f is decreasing from x = -3.5 to x = 0, then increasing from x = 0 to x = 3.5. Therefore, the statement "the function is decreasing on the interval [-3, 3]" is false.

Question 15

Determine all values of x at which the function is discontinuous.

Accepted Answer

The answer of Determine all values of x at which...

Question 16

Determine all values of x at which the function is discontinuous.

Accepted Answer

A function is discontinuous at a point if it exhibits at least one of the three types of discontinuities: removable, jump, or infinite. However, looking at the given function, it has no points or values that make it have either of the discontinuities, so it must be continuous everywhere. Thus, the answer is none of the given choices.

Question 17

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

Accepted Answer

The answer of The function P, whose graph follows, gives...

Question 18

Find the one-sided limit, if it exists.

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 19

Find the one-sided limit, if it exists.

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 20

The function that gives the cost of a certain commodity is defined by  where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C. Determine the values of x for which the function C is discontinuous.

Accepted Answer

The answer of The function that gives the cost of...

Quiz 2: Functions, Limits and the Derivative

Find the values of x for which the function is continuous.

Find the values of x for which the function is continuous.

Use the graph of the function f to find and if the limit exists.

Determine all values of x at which the function is discontinuous.

Find and , where .

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Use the graph of the function f to find and if the limit exists.

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Find the one-sided limit, if it exists.

Find and , where

The base salary of a salesman working on commission is $13,000. For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Find the indicated one-sided limit.

Let . Find the zeros of f in by solving the equation .

Refer to the graph of the function f and determine whether the statement below is true or false.

Determine all values of x at which the function is discontinuous.

Determine all values of x at which the function is discontinuous.

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

Find the one-sided limit, if it exists.

Find the one-sided limit, if it exists.

The function that gives the cost of a certain commodity is defined by where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C. Determine the values of x for which the function C is discontinuous.