Evaluate the following:
(i) \(\lim \limits_{x \to 0} \cfrac{sin \,ax}{sin \,bx}\)
lim (sin ax)/(sin bx), [x∈0]
(ii) \(\lim \limits_{x \to 0}\)\(\cfrac{sin^2 3x}{x^2}\)
lim (sin^2 3x)/(x^2), [x∈0]
(iii) \(\lim \limits_{x \to 0}\) \(\cfrac{1-cos x}{x^2}\)
lim (1-cosx)/(x^2), [x∈0]
(iv) \(\lim \limits_{x \to \pi}\) \(\cfrac{sin(\pi -x)}{\pi(\pi - x)}\)
lim sin(π - x)/π(π - x), [x∈ π]
(v) \(\lim \limits_{x \to 0}\) \(\cfrac{ax + x\,cosx}{bsinx}\)
lim (ax + xcos x)/(bsinx), [x∈0]
(vi) \(\lim \limits_{x \to 0}\) \(\cfrac{cos\,2x - 1}{cos \,x -1}\)
lim (cos 2x -1)/(cos x -1), [x∈0]
(vii) \(\lim \limits_{x \to \frac{\pi}{2}}\) \(\cfrac{tan 2x}{x - {\frac{\pi}{2}}}\)
lim (tan2x)/(x -π/2), [x∈ π/2]