Home
Class 12
MATHS
Evaluate: lim(x->a)(logx-loga)/(x-a)...

Evaluate: `lim_(x->a)(logx-loga)/(x-a)`

Text Solution

Verified by Experts

Let `x-a=h.` Then if `xtoa, hto0.` Therefore,
`underset(xtoa)lim(logx-loga)/(x-a)" "`(0/0 form)
`underset(hto0)lim(log(a+h)-loga)/(h)`
`underset(hto0)lim(log(1+(h)/(a)))/((h)/(a)a)=(1)/(a)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.1|10 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)(logcosx)/x

Evaluate: lim_(x->2)(x-2)/((log)_a(x-1))

Evaluate: lim_(x->a)("log"(x-a))/(log(e^x-e^a))

Evaluate: lim_(x->0)(e^x-1-x)/(x^2)

Evaluate: lim_(x->2) (x^2-1)/(2x+4)

Evaluate: lim_(x->0)(cosx)^(cotx)

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate: lim_(x->0)(x2^x-x)/(1-cosx)

Evaluate: lim_(xrarr0)x^x

Evaluate: lim_(x rarr 1) (e^(logx)-1)/(e^(x-1)-1)