G(x) ds 0. 0.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.1: Functions And Function Notation
Problem 8TI: Using Figure 7, solve f(x)=1 .
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Let G(x) be given, where f is continuous for all real t. Find (a) G(0), (b) G′(0), (c) G″(x), and (d) G″(0).

G(x)
ds
0.
0.
Transcribed Image Text:G(x) ds 0. 0.
Expert Solution
Step 1

 

 

(a)

The given function Gx=0xs0sf(t)dtds where f is continuous for all real values of t.

The integration is performed as,

abf(x)dx=g(x)ab

In the function, G(x) interchange the value of x with 0.

So, 

G0=00s0sf(t)dtds=0

 

Step 2

(b)

According to the second fundamental theorem of calculus, ddxaxf(t)dt=f(x).

Let Fs=s0xf(t)dt.

Thus, Gx=0xFsds.

Now,

G'x=Fx=x0xf(t)dtG'0=000f(t)dt=0

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