Find the Linearization

Question

Find the linearization of y = tan⁻¹(5x) at x = 2.

L(x) =

Answer 1

Greetings! Lets solve this problem shall we !?

We yield the formula for the Linearization such that

L(x) = f(a) + f'(a)(x-a) ... since x = 2 we let a equal to 2 such that

L(2) = f(2) + f'(2)(x-a)

= tan^-1(5*2) + (1/(2)²+1)(x-2)

= 1.47 + (1/5)(x-2)

= 1.47 + (1/5)x - (2/5)

L(2) = (1/5)x + 1.07

I hope this helped!