Home
Class 11
MATHS
For xgt0, lim(xto0) {(sinx)^(1//x)+((1)/...

For `xgt0, lim_(xto0) {(sinx)^(1//x)+((1)/(x))^sinx}`, is

Text Solution

Verified by Experts

`lim_(x->o^+)(sinx)^(1/x)+(1/x)^(sinx)`
let`L=lim_(x->0^+)(1/x)^sinx`
`lnL=lim_(x->0^+)sinx ln(1/x)`
`=lim_(x->0)ln(1/x)/(cosecx)`
LH hospital
`lnL=(x(1/x^2))/cot^2x=1/(xcot^2x)=tan^2x/x`
`lim_(x->0^+)tanx/x*tanx=0`
`lnL=0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

For xgt0, lim_(xrarr0) {(sinx)^(1//x)+((1)/(x))^sinx} , is

For xgt0, lim_(xrarr0) {(sinx)^(1//x)+((1)/(x))^sinx} , is

lim_(xto0)(e^(sinx)-1)/x=

lim_(xto0)(sinx(1-cosx))/x^(3)

lim_(xto0)(tanx-sinx)/x^(3)

lim_(xto0)(2"arc"sinx)/(3x)

lim_(xto0)(xe^(x)-sinx)/x is

Evaluate: lim_(xto0)(sinx+cosx)^(1//x)

lim_(xto0) (sinx^(@))/(x) = _________

lim_(xto0)(((1+x)^(1//x))/e)^(1/(sinx)) is equal to