Evaluate : $\displaystyle{\lim_{x \to 0}}$ $x^3 cotx\over {1-cosx}$

Solution :

$\displaystyle{\lim_{x \to 0}}$ $x^3 cosx\over {sinx(1-cosx)}$

= $\displaystyle{\lim_{x \to 0}}$ $x^3 cosx(1 + cosx)\over {sinxsin^2x}$

= $\displaystyle{\lim_{x \to 0}}$ ${x^3\over sin^3x}.cosx(1 + cosx)$ = 2

---

Similar Questions

Evaluate the limit : $\displaystyle{\lim_{x \to \infty}}$ $x^2 + x + 1\over {3x^2 + 2x – 5}$

Evaluate : $\displaystyle{\lim_{x \to \infty}}$ $({7x^2+1\over 5x^2-1})^{x^5\over {1-x^3}}$

Evaluate : $\displaystyle{\lim_{x \to 0}}$ $xln(1+2tanx)\over 1-cosx$

Evaluate : $\displaystyle{\lim_{x \to 0}}$ $(2+x)sin(2+x)-2sin2\over x$

If $\displaystyle{\lim_{x \to \infty}}$(${x^3+1\over x^2+1}-(ax+b)$) = 2, then find the value of a and b.