Question

Lim x-> 4 {3-Sqrt(5 + x)}/ {1-Sqrt(5 - x)} without using L' hospital rule

Answer 1

\[\lim_{x \rightarrow 4} \frac{ 3-\sqrt{5 + x}}{1-\sqrt{5 - x}}\]

Answer 2

i'd probably say multiply num and denum by their conjugates first :)

Answer 3

do u know about conjugate?

Answer 4

yes.. i multiplied the num and denum with the conjugate of denum

Answer 5

do the same thing with the conjugate of num and see what happens

Answer 6

ok ..will try and check in a while

Answer 7

good :)

Answer 8

@mukushla i am getting sqrt(x+5)-3
----------- which is again in 0/0 form
sqrt(5-x)-1

Answer 9

can u plz check it again, u must come up with\[-\frac{\sqrt{x+5}+3}{\sqrt{5-x}+1}\]

Answer 10

sorry\[-\frac{\sqrt{5-x}+1}{\sqrt{x+5}+3}\]

Answer 11

@mukushla I am not getting this ,could you please show me the steps ?

Answer 12

sure

Answer 13

\[\lim_{x \rightarrow 4} \frac{ 3-\sqrt{5 + x}}{1-\sqrt{5 - x}}\]\[=\lim_{x \rightarrow 4} \frac{ \color\red{3-\sqrt{5 + x}}}{\color\green{1-\sqrt{5 - x}}}\frac{ \color\red{3+\sqrt{5 + x}}}{3+\sqrt{5 + x}}\frac{ 1+\sqrt{5 -x}}{\color\green{1+\sqrt{5 - x}}}\]\[=\lim_{x \rightarrow 4} \frac{\color\red{4-x}}{\color\green{x-4}}\frac{ 1+\sqrt{5 - x}}{3+\sqrt{5 + x}}\]\[=\lim_{x \rightarrow 4} -\frac{ 1+\sqrt{5 - x}}{3+\sqrt{5 + x}}\]now plug the value\[=-\frac{2}{6}=-\frac{1}{3}\]