Home
Class 11
MATHS
Let m and n be two positive integers gre...

Let m and n be two positive integers greater than 1.If `lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2)` then the value of `m/n` is

Text Solution

Verified by Experts

`lim_(alpha->0)(e(e^(cosalpha^n)-1))/(alpha^m)`
`=lim_(alpha->0)(e(cosalpha^n-1)/alpha^m)`
`=-elim_(alpha->0)(1-cosalpha^n)/alpha^m`
`=-2elim_(alpha->0)(sin(alpha^n)/2*sin(alpha^n)/2)/(alpha^n/2*alpha^m*alpha^n/2)`
`=2e*alpha^(2n)/(4alpha^m`
`alpha^(2n-m)=1`
`2n-m=0`
`m/n=2`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let m and n be two positive integers greater than 1. if lim_(alphararr0)((e^cos(a^n)-e)/alpha^m)=-(e/2) ,then the value of m/n is

Let m and n be two positive integers greater than 1. If underset(alphato0)lim((e^(cos(alpha^(n)))-e)/(alpha^(m)))=-((e)/(2))" then the value of "(m)/(n)" is-"

Let m and n be the two positive integers greater than 1 . If underset( alpha rarr 0 ) ( "lim")((e^(cos(alpha^(n)))-e)/(alpha^(m))) = -((e )/( 2)) then the value of ( m )/( n ) is

lim_(alpha to 0) (sin (alpha^n))/((sin alpha)^(m))

lim_(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))

lim_(x rarr0)(e^(cos x^(n))-e)/(x^(m))=-(e)/(2) then find (4m)/(5n)

Lt_(alpha to 0) (sin(alpha^(n)))/((sin alpha)^(m))=(m, n N)=0 if

If cot alpha+tan alpha=m and (1)/(cos alpha)-cos alpha=n, then