Question

If `lim_(xto oo)([f(x)]+x^(2)){f(x)}=k`, where `f(x)=(tanx)/x` and `[.],{.}` denote geatest integer and fractional part of x respectively, the value of `[k//e]` is ………..

Answer 1

Answer:

Assume that limx→a f(x)=K and limx→a g(x)=L exist and that c is any constant. Then,

limx→a [cf(x)]=c limx→a f(x)=cK

limx→a [f(x)±g(x)]= limx→a f(x)± limx→a g(x)=K±L

limx→a [f(x)g(x)]= limx→a f(x) limx→a g(x)=KL

limx→a [

f(x)

g(x)

]=

limx→a f(x)

limx→a g(x)

=

K

L

,provided L= limx→a g(x)≠0

limx→a [f(x)]n=[ limx→a f(x)]n=Kn,where n is any real number

limx→a [n

√

f(x)

]=n

√

limx→a f(x)

limx→a c=c

limx→a x=a

limx→a xn=an