LIMITS: If f(x)=(2(x^2))+3x+5 find the lim h->0 (f(h)-f(0))/h

Please help me answer this question, any help would be appreciated. Thank you so much.

f(x + h) = 2 * (x + h)^2 + 3 * (x + h) + 5 = 2 * (x^2 + 2hx + h^2) + 3x + 3h + 5 = 2x^2 + 4hx + 2h^2 + 3x + 3h + 5

f(x) = 2x^2 + 3x + 5

f(x + h) - f(x) =>
2x^2 + 4hx + 2h^2 + 3x + 3h + 5 - 2x^2 - 3x - 5 =>
4hx + 2h^2 + 3h

Divide by h

4x + 2h + 3

Let h go to 0

4x + 3

x = 0

4 * 0 + 3 =>
0 + 3 =>
3

Congratulations! You just took a step into the cesspool known as Calculus!

By definition of derivative,
lim h->0 (f(h)-f(0))/h = f'(0) = 3