How do you evaluate #\lim _ { x \rightarrow 6} \frac { 2x - 12} { \sqrt { 3x + 7} - 5}#?

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Answer 1 · 2017-09-13T17:36:19

# 20/3.#

Here is a way to find the Reqd. Limit, say L, without using

L'Hospital's Rule.

# L=lim_(x to 6) (2x-12)/{sqrt(3x+7)-5},#

#=lim_(x to 6) (2x-12)/{sqrt(3x+7)-5}xx{sqrt(3x+7)+5}/{sqrt(3x+7)+5},#

#=lim_(x to 6) {2(x-6)(sqrt(3x+7)+5)}/{(3x+7)-25},#

#=lim_(x to 6) {2cancel((x-6))(sqrt(3x+7)+5)}/{3cancel((x-6))},#

#=lim_(x to 6) 2/3*(sqrt(3x+7)+5),#

#=2/3*(sqrt(3*6+7)+5),#

#=2/3*(5+5),#

# rArr L=20/3.#

Enjoy Maths.!