Question

Calculus????????

Find the linear approximation that is represented by L(x) for the function:

f(x)= (1+x)^6 at x=0

What does the Error formula give as a rough estimate for the error at x=0.1

Answer 1

`f(x)=(1+x)^6\implies f'(x)=6(1+x)^5\implies f'(0)=6`

At
`x=0`, you get
`f(0)=(1+0)^6=1`, so the tangent line to
`f` at this point is


`y-1=6(x-0)\implies y=6x+1`

which suggests
`f(0.1)\approx6*0.1+1=1.6`