Question

Find the linear approximation of the function
f(x) = 1 − x at a = 0.
a) L(x)-?
b) Use L(x) to approximate square root of 0.9 (Round your answers to four decimal places.)

Answer 1

Racist user alert.

Answer 2

^?

Answer 3

you've missed out on the last few posts..

Answer 4

will look into it

Answer 5

he posts under nazyma though..

Answer 6

@Nazym do you want to learn how to do linear approximations?

Answer 7

Omg what did I do to you? Where am I being racist???

Answer 8

Oh sorry, it's actually square root of 1 − x at a = 0.

Answer 9

interesting.....he gets blackballed and decided to create a new account....

Answer 10

The linear approximation of a function f(x) at x = a is\[L(x)=f(a)+f \prime(a)(x -a)\]where L(x) is the linearization of f at a.

Example:
Find the linear approximation of\[f(x)=\sqrt{x -2}\]at a = 6

Solution:\[f \prime(x)=\frac{ 1 }{ 2\sqrt{x -2} }\]
\[f \prime(6)=\frac{ 1 }{ 4 }\]and\[f(6)=4\] Now\[L(x) =f(6)+f \prime(6)(x -6)\]
\[L(6)=4+\frac{ 1 }{ 4 }(x -6)\]
\[L(6)=4+\frac{ 1 }{ 4 }x -\frac{ 3 }{ 2 }\]
\[L(6)=\frac{ 1 }{ 4 }x+\frac{ 5 }{ 2 }\]Therefore the corresponding linear approximation is\[\sqrt{x -2}\approx \frac{ 1 }{ 4 }x +\frac{ 5 }{ 2 }\]
Let me know if this helps!!