limits question please help|||||||||||||||||||||

Question

find lim (sqr(x+5)-sqr(5))/x as x approaches 0

 

Answer 1

lt      sqrt (x+5)-sqrt5 / x

x→0

⇒lt        sqrt (x+5)-sqrt5 / x *sqrt(x+5)+sqrt5 / sqrt(x+5)+sqrt5

x→0

⇒lt        (x+5)-5 / x*sqrt(x+5)+sqrt5

x→0

⇒lt           x /x*sqrt(x+5)+sqrt5

x→0

⇒lt         1 / sqrt(x+5)+sqrt5

x→0

⇒1 / sqrt(0+5)+sqrt5

⇒1 / sqrt5+sqrt5

⇒1/2*sqrt5

lt        sqrt(x+5)-sqrt5 / x  =1 /2*sqrt5

x→0