y=1-x+x^2/2!-x^3/3!....to infinity find d^2y/dx^2
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✔ 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...
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...
Anonymous:
thanks bhai
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