Question

L'Hospital rule.

Answer 1

L HOSPITAL'S RULE

While evaluating limit if we get indeterminate form i.e ($\frac {0} {0})$ ) form or ( ∞/ ∞) form then we can evaluate the limit by differentiating numerator and denominator. We will differentiate it every time we get that indeterminate form after differentiation of numerator and denominator until we get the desire form i.e not ($\frac {0} {0} )$ ) form or (∞/∞) form.This is L HOSPITAL'S RULE.

EXAMPLE - lim($x$ $\to$ 0) ($\frac {sinx} {x} )$ It is in ($\frac {0} {0})$ ) form as sin(0)=0

So L Hospital's rule is applicable

=lim($x\to0)\frac {d/dx (sinx)} {d/dx (x)}$

=lim$(x\to0)$ ( $\frac {cosx} {1})$

=lim($x\to0) (cosx)$

=$cos(0)=1$ (ans)