Which of the following?

Question

Which of the following is the quadratic approximation for f(x)=e^-x at x=0? 

 

a) 1-x+(1/2)x^2

b) 1-x-(1/2)x^2

c) 1+x+(1/2)x^2

d) 1+x

e) 1-x

 

Answer: A

 

Please show all your work. Thanks.

Answer 1

f(x) = e^(-x)  

 

The Formula for Quadratic Approximation at x = 0,

           f(x) ~ f(0) + f'(0)(x-0) + (1/2)f''(0)(x-0)^2    where f(0) = 1,  f'(0) = -1,  f"(0) = 1

Therefore f(x) ~ 1 - x + (1/2)x^2