contestada

Use linear approximation, i.e. the tangent line, to approximate 10.1 2 10.12 as follows: Let f ( x ) = x 2 f(x)=x2 and find the equation of the tangent line to f ( x ) f(x) at x = 10 x=10.

Respuesta :

LammettHash

The linear approximation of a function [tex]f(x)[/tex] centered at [tex]x=a[/tex] is

[tex]L(x)=f(a)+f'(a)(x-a)[/tex]

We have

[tex]f(x)=x^2\implies f'(x)=2x[/tex]

and we want to find [tex]L(10.1)[/tex] for [tex]a=10[/tex].

Since [tex]f(10)=100[/tex] and [tex]f'(10)=20[/tex], we get

[tex]10.1^2\approx L(10.1)=100+20(10.1-10)=102[/tex]

Compare this to the actual value of [tex]10.1^2=102.01[/tex].

Otras preguntas