lim[x3/2- 27] / [x-9] x tends to 9 - Maths - Continuity and Differentiability

Question

lim[x3/2- 27] / [x-9]
x tends to 9

Ajanta Trivedi · Accepted Answer

the given limit is: $\lim_{x \to 9} (\frac{x^{3 / 2} - 27}{x - 9})$

the above limit is of the form 0/0.

so applying L'Hospital Rule: (differentiating the numerator and denominator)

$\lim_{x \to 9} \frac{\frac{3}{2} x^{3 / 2 - 1} - 0}{1} = \lim_{x \to 9} [\frac{3}{2} x^{1 / 2}] = \frac{3}{2} * (9)^{1 / 2} = \frac{3}{2} * 3 = \frac{9}{2}$

hope this helps you.

cheers!!