Question

If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = ______

Options

• x

• -x

• -y

• y

Answer 1

If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = y

Explanation:

y = `1 + x + x^2/((2)!) + x^3/((3)!) + ....`

⇒ y = e^x ............(i)

∴ `dy/dx = e^x`

∴ `(d^2y)/(dx^2) = e^x = y` .................[From (i)]