PigMeat:
That you all @ cooboy ndsmelody efewestern y'all contributions were really helpful
.
Here is another question
(1) Prove that limx~>0 (sinx/x)=1
(2) Evaluate limx~>0 (x^3+x^2/x^2)

Using l'hopitals rule
(1) Lim x->0 (sinx/x), (sin (0)/0) =0 dy/dx = lim x->0 (cosx/ 1)


Lim x->0 ( cos (0)/1) = 1/1 = 1..

2.
Using same l'hopitals rule
Lim x-> 0 (x^3+x^2/x^2) =0 , dy/dx = lim x->0 (3x^2+2x/2x) = (3(0)^2+2(0)/2(0)) = 0. We reapply l'hopitals rule again to get a variable answer
Dy/Dx Lim x->0 (6x+2/2) (6(0)+2/2) = 1...

Mad I'm late to answer this