L Hospital rule

D L Hopital rule to solve limit & Illustration , 1^infinity Based question ( 2 Methods )

Find the following using L'Hospital's rule (i) lim_(xto0) ((16+5x)^(1//4)-2)/((32+3x)^(1//5)-2)" "(ii)lim_(xto pi//2) [xtanx-(pi//2)secx]

Statement-1: If the graph of the function y=f(x) has a unique tangent at the point (a, 0) through which lim_(x->a) log_e (1+6(f(x)))/(3f(x))=2 Statement-2: Since the graph passes through (a, 0). Therefore f(a) = 0. When f(a) = 0 given limit iszero by zero form so that it can be evaluate by using L-Hospital's rule.

Find the values of a and b in order that lim_(x->0) (x(1+a cos x)-b sinx)/x^3=1 [using L' Hospital' srule].

Using L'Hospital 's rule prove that lim_(theta rarr 0) (theta-sintheta)/(theta^3)=1/6

L'Hopital Rule || Zero and Infinite Forms OF Limit

Hospitable

How to apply condition on :L'Hopital' Rule For Evaluating Limits

What is wrong with the following application of L'Hopital's rule ? lim_( x to 0+) (sin x)^x

What is wrong with the following application of L'Hopital's rule ? lim_( xto 0) (1-3x)^(4//x)