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Chapter 14: Q. 7 (page 907)

Determine the value for k that will make the function continuous atc=4 f(x)=x2-9x+3ifx鈮�4kx+5ifx>4

Short Answer

Expert verified

The value ofk=-1

Step by step solution

01

Step 1. Value of the function at c=4

The function wherec=4is

f(x)=x2-9x+3

Substituting the values,

f(4)=42-94+3=77=1

02

Step 2. Apply the limit for c<4

On applying the limit, we get,

limx鈫�4-x2-9x+3=limx鈫�4-(x+3)(x-3)x+3

=limx鈫�4-(x-3)=4-3=1

03

Step 3. Apply the limit for c>4

On applying the limit,

limx鈫�4+(kx+5)=limx鈫�4+kx+limx鈫�4+5=klimx鈫�4+x+limx鈫�4+5=4k+5

04

Step 4. Value of k

We know, if a continuous limit exists then

limx鈫�4-f(x)=limx鈫�4+f(x)=limx鈫�4f(x)1=4k+5-4=4k-1=k

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Most popular questions from this chapter

Use the graph shown to determine if the limit exists. If it does, find its value.

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
limx鈫�0f(x),f(x)=x-1ifx<03x-1ifx鈮�0

In Problems 7鈥� 42, find each limit algebraically

limx鈫�1(-3)

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Findlimx鈫�-4+f(x).

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�-1f(x),f(x)=1x
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