Using linear approximation find A and B

Question

The linear approximation at x=0 to √(8+8x) is A+Bx

where A is? 

and B is?

Answer 1

Dalia,

          A series expansion of the function f(x) at x=0 is f(0)+xf^'(0)+higher order terms. f^'(0) is the first derivative of f(x) at x=0.

     The linear expansion is just the first two terms and f(x)=√(8+8x) so f^'(x)=(1/2*8)/√(8+8x) and f(0)=4/(2*√2)=2/√2 and f(0)=2√2.

 

So A=f(0)=2√2 and B=f^'(0)=2/√2=√2

 

Jim