Home
Class 12
MATHS
Evaluate lim(xto0^(+)) x^(m)(logx)^(m),m...

Evaluate `lim_(xto0^(+)) x^(m)(logx)^(m),m,n,inN.`

Text Solution

Verified by Experts

`underset(xto0^(+))limx^(m)(logx)^(n)" "(0xxoo" form")`
`=underset(xto0^(+))lim((logx)^(n))/(x^(-m))" "((oo)/(oo)" form")`
`=underset(xto0+)lim(n(logx)^((n-1))(1)/(x))/(-mx^(-m-1))" "`(Using L'Hospital's rule)
`=underset(xto0+)lim(n(logx)^(n-1))/(-mx^(-m))" "((oo)/(oo)" form")`
`underset(xto0+)lim(n(n-1)(logx)^((n-2))(1)/(x))/((-m)^(2)x^(-m-1))" "`(Using L'Hospital's rule)
`=underset(xto0+)lim(n(n-1)(logx)^(n-2))/(-m^(2)x^(-m))" "((oo)/(oo)" form")`
`=underset(xto0+)lim(n!)/((-m)^(n)x^(-m))=0" "("Differentiating "N^(r)" and "D^(r)" n times")`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.1|10 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.2|7 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Comprehension Type|4 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate: lim_(x->0)x^m(logx)^n ,m , n in Ndot

Evaluate lim_(xto0) (logcosx)/(x)

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

Evaluate lim_(xto0) (x)^((1)/(log_(e)sinx)).

Evalaute lim_(xto0) (x2^(x)-x)/(1-cosx)

Evaluate lim_(xto0) (e^(x^(2))-cosx)/(x^(2))

Evaluate lim_(xto0) (sinx-x)/(x^(3)).

Evaluate: lim_(xto0)(cosx)^(cot^(2)x)

Evaluate lim_(xto0^(+)) (1)/(x)cos^(-1)((sinx)/(x)) .

Evaluate: lim_(xto0)(e^(ax)+e^(Bx)-2)/(x)