Question

Let `f: R->[0,oo)` be such that `lim_(x->5) f(x)` exists and `lim_(x->5) ((f(x))^2-9)/sqrt(|x-5|)=0` then `lim_(x->5)f(x)=`
A. 1
B. 2
C. 3
D. 0

Answer 1

Correct Answer - C
`lim_(xto5)((f(x))^2-9)/(sqrt(|x-5|))=0`
` rArr lim_(xto5)(f(x))^2-9=0`
` rArr l^2-9=0, "where" lim_(xto5)f(x)=l`
`rArr l= +-3`
`rArr l=3 [because f(x)ge 0 " for all " x in R ]`
`rArr lim_(xto5)f(x)=3`