4 Answers
106Q1.1.4 Let lim(x→a)f(x) = -y (y>0)
then frm given condition, we have -y+1/y=0
or y2=1
or y=1 (y>0)
So lim(x→a)f(x) = -1
(thx virang)
62take x=1/ar x0
when x tends to zero... r becomes very large
use this recurrsively in the expression to get
f(x) = b-r f(x0)
so, limit x-> f(x) = lim r-> infinity b-r f(x0)
which gives zero :)
241.1.3
\lim_{x\rightarrow 0}[f(x)+\frac{1}{f(x)}]=2
=>\lim_{x\rightarrow 0}f(x)+\lim_{x\rightarrow 0}\frac{1}{f(x)}=2
=>\lim_{x\rightarrow 0}f(x)+\frac{1}{\lim_{x\rightarrow 0}f(x)}=2
Now take \lim_{x\rightarrow 0}f(x)=t
and solve the quadratic eqn
