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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

Sketch the graph of the function

f(x) = { 2 x 3  if       2 + 3    if   x   >   2

and evaluate lim x a + f(x), lim x a f(x), and lim x a f(x) at the point a = 2, if the limits exist.

To determine

To sketch: The graph of the given function and evaluate limxa+f(x) , limxaf(x) and limxaf(x) at the point a=2 , if limit exists.

Explanation

Given:

The given function is,

f(x)={2x3ifx2x+3ifx>2 (1)

Calculation:

Substitute different values of x and find the corresponding values to the function respectively.

Substitute 0 for x in equation (1) to find the value of f(x) ,

f(0)=203=03=3

Substitute 1 for x in equation (1) to find the value of f(x) ,

f(1)=213=23=1

Substitute 1.5 for x in equation (1) to find the value of f(x) ,

f(1.5)=2(1.5)3=33=0

Substitute 2 for x in equation (1) to find the value of f(x) ,

f(2)=223=43=1

Substitute 3 for x in equation (1) to find the value of f(x) ,

f(3)=3+3=0

Substitute 4 for x in equation (1) to find the value of f(x) ,

f(4)=4+3=1

Substitute 5 for x in equation (1) to find the value of f(x) ,

f(5)=5+3=2

From above calculation substitute different values of x and f(x) in a table which is given below,

x f(x)
0 3
1 1
1

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P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-1BMCh-2 P-2BMCh-2 P-3BMCh-2 P-4BMCh-2 P-5BMCh-2 P-6BM

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