Question

For the function f(x) = sin(3x) + x^2 + 5, a. Demonstrate that this relationship is non-linear. (Check both requirements) b. Linearise the relationship about an operating point of Xo = 1.2 rad.

Answer 1

Answer:

a.It is not a linear equation

b.L(x)=4.5 +5.7(x-1.2)  

Explanation:

Given that

$f(x)=sin 3x+x^2+5$

The function f(x) contains power of x more than 1 that is why it is not a linear function.This is a non-linear function.

To linearise the function

$L(x)={f(a)}'+(x-x_o)f(a)$

Given that

$x_o=1.2 rad$  ⇒a=1.2

a=68.85°

${f(a)}'=3 cos 3x +2x$

By putting the values

${f(a)}'=3 cos 3\times 68.85 +2\times 1.2$

${f(1.2)}'=4.5$

$f(1.2)=sin 3\times 68.85+1.2^2+5$

f(1.2)=5.7

$L(x)={f(a)}'+(x-x_o)f(a)$

L(x)=4.5 +(x-1.2) x 5.7

L(x)=4.5 +5.7(x-1.2)