BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1, Problem 16P
To determine

To describe: Whether “f(g+h)=fg+fh” is true or false.

Expert Solution

Answer to Problem 16P

Solution:

f(g+h)=fg+fh is false.

Explanation of Solution

Let f(x)=cosx,g(x)=x and h(x)=x.

Substitute,f(x),g(x) and h(x) in left side of the statement,

[f(g+h)](x)=cos(x+x)=cos2x=cos2xsin2x

Substitute,f(x),g(x) and h(x) in right side of the statement,

(fg)(x)+(fh)(x)=cosx+cosx=2cosx

Observe that the two sides are not equal.

Thus, the statement given is false.

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