Evaluate the following:
(i) \(\lim \limits_{x \to 0} \cfrac{e^{ax}-1}{e^{bx}-1}\)
lim (e^ax - 1) / (e^bx - 1) [x ∈ 0]
(ii) \(\lim \limits_{x \to 0} \cfrac{log(1+x)}{sin x}\)
lim (log(1+x)) / sinx [x ∈ 0]
(iii) \(\lim \limits_{x \to 0} \cfrac{e^{x}+e^{-x}-2}{x^2}\)
lim (e^x + e^-x -2) / x^2 [x ∈ 0]
(iv) \(\lim \limits_{x \to 0} \cfrac{e^{x}- sinx -1}{x}\)
lim (e^x + sinx -1) / x [x ∈ 0]
(v) \(\lim \limits_{x \to 0} \cfrac{e^{sin x}- 1}{log(1+x)}\)
lim (e^sinx -1) / log(1+ x) [x ∈ 0]