Answer to Question #292333 in Calculus for Mistura

Question

What is the coefficient of x^5 in y = Sinh(X)

Answer 1

Solution:

We know that,

$\sinh x=x+\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+\dfrac{x^7}{7!}+\dfrac{x^9}{9!}+...$

Then, coefficient of $x^5=\dfrac{1}{5!}=\dfrac{1}{120}$