Question

y=1-x+x^2/2!-x^3/3!....to infinity find d^2y/dx^2

Answer 1

✔ Since the number of terms is finite, just differentiate term by term using the power rule.

dy/dx = 0 + 1 + 2x/2! + 3x^2/3! + ... to infinity

dy/dx = 0 + 1 + 2x/2! + 3x^2/3! + ... + nx^(n-1)/n!

dy/dx = 1 + x + x^2/2! + ... + x^(n-1)/(n -1)!

✔ Compare dy/dx to y and note that the last term of y, which is xn/n!, is not in dy/dx, while all the other terms of y are in dy/dx.

✔ Then,

dy/dx = y - x^n/n.

d^2y/dx^2 = dy/dx - n.1/n. x^(n-1)

d^2y/dx^2 = dy/dx - x^(n-1)

d^2y/dx^2 = (x^n)/n - x^(n-1)

✔ hope this will help u..

@Neha...