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Determine the values of x for which the function f(x)=2x2−25x is continuous

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Determine the values of x for which the function

f(x)=2x2−25x

is continuous. If the function is not? continuous, determine the reason.

Where is the function continuous or not? continuous?

A.The function is not continuous at

x=25.

B.

The function is continuous for all values of x.

C.The function is not continuous at

x=0.

D.The function is not continuous at

x=0

and

x=25.

Your answer is correct.

E.The function is continuous for all values of x less than

2.

F.The function is not continuous at

x=2.

G.The function is continuous for all values of x between 0 and

2.

H.

The function is continuous for all values of x greater than 0.

Why is the function continuous or not? continuous?

A.

The function exists for all points and any small change in x produces only a small change in? f(x).

B.The function does not exist at the point

x=2.

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Determine the values of x for which the? function, as represented by the graph to the? right, is continuous. If the function is not? continuous, determine the reason.

-55-55xy       A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. The curve rises from the third quadrant and crosses the y-axis at (0, 1) and then continues to rise.

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

The function is continuous for all values of x. The function exists for all points and any small change in x produces only a small change in? f(x).

Your answer is correct.

B.The function is not continuous at

x=nothing

because a small change from this value of x may produce a large change in? f(x).

?(Use a comma to separate answers as? needed.)

C.The function is not continuous at

x=nothing

because the function does not exist there.

?(Use a comma to separate answers as? needed.)

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Determine the values of x for which the? function, as represented by the graph to the? right, is continuous. If the function is not? continuous, determine the reason.

-55-55xy       A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A graph has two branches. The first branch is a ray that falls to the left from an open circle at (negative 1, negative 1). The second branch is a curve that increases at an increasing rate from left to right, starting at a closed circle at (negative 1, 3).

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.The function is not continuous at

x=negative 1−1

because a small change from this value of x may produce a large change in? f(x).

?(Use a comma to separate answers as? needed.)

Your answer is correct.

B.The function is not continuous at

x=nothing

because the function does not exist there.

?(Use a comma to separate answers as? needed.)

C.

The function is continuous for all values of x. The function exists for all points and any small change in x produces a small change in? f(x).

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Evaluate the indicated limit by evaluating the function for values shown in the table and observing the values that are obtained. Do not change the form of the function.

limx→2x3−4xx−2

x	1.900	1.990	1.999	2.001	2.010	2.100
?f(x)	7.417.41	7.94017.9401	7.99407.9940	8.00608.0060	8.06018.0601	8.618.61

?(Type integers or decimals rounded to four decimal places as? needed.)

limx→2f(x)=88

?(Type an integer or a? decimal.)

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Evaluate the following limit by direct evaluation. Change the form of the function if necessary.

limx→0 x5+7xx

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

limx→0 x5+7xx=77

?(Simplify your? answer.)Your answer is correct.

B.

The limit does not exist.

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Determine if the following limit exists. Compute the limit if it exists.

limx→−7

x2−49x+7

Select the correct choice below and fill in any answer boxes in your choice.

A.

limx→−7x2−49x+7=negative 14−14

Your answer is correct.

B.

The limit does not exist.

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Evaluate the following limit by direct evaluation. Change the form of the function if necessary.

limh→8h3−512h−8

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

limh→8h3−512h−8=192192

?(Type an integer or a simplified? fraction.)Your answer is correct.

B.

The limit does not exist.

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Evaluate the following limit by direct evaluation. Change the form of the function if necessary.

limx→1(8x−4)2−162x−2

Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

limx→1(8x−4)2−162x−2=3232

?(Type an integer or a simplified? fraction.)Your answer is correct.

B.

The limit does not exist.

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For the limit? below, evaluate the function at? 0.1, 0.01, and 0.001 from both sides of the value it approaches. From these? values, determine the limit.? Then, by using an appropriate change of algebraic? form, evaluate the limit directly.

limx→0x3+4x2x2

Complete the table below to evaluate the function at? 0.1, 0.01, and 0.001 from both sides of the value it approaches.

x	−0.1	−0.01	−0.001	0.001	0.01	0.1
f(x)	3.93.9	3.993.99	3.9993.999	4.0014.001	4.014.01	4.14.1

?(Type integers or? decimals.)

Evaluate the limit using these table values and directly.

limx→0x3+4x2x2=4