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Chapter 4: Q. 08 (page 364)

Preview of Differential Equations:

Given each of the following equations involving a functionf, find a possible formula for f(x).

f'(x)=2f(x)

Short Answer

Expert verified

The possible formula for the function f'(x)=2f(x)is f(x)=e2x.

Step by step solution

01

Step 1. Given Information.

The function:

f'(x)=2f(x)

02

Step 2. Consider the function.

Consider the function,

f(x)=e2xf'(x)=ddxe2x=2e2x=2f(x)

So the function isf(x)=e2x.

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Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on [-π2,2π]?

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