Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 400 off


Lim(x tends to infinity)(sin-1x-tan-1 x)2/xn exists  for maximum value of n, is

a. n=2



d.No such value of n is possible

7 years ago


Answers : (1)


For any values of x , sin-1x  lies in ( -Pi/2, Pi/2 )

also ,  -Pi/2 <  tan-1x  < Pi/2

and here as x tends to infinity , tan-1x = Pi/2

therefore, as x tends to infinity , (sin-1x - tan-1x)2 becomes some positive number( >=0 )

also xn goes to +infinity for any value of n(n>0)

so, the final limit to zero ( i.e., limit exists ) for all n>0

from the options max alue of n is 6

so,option C


Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best.


Naga Ramesh

IIT Kgp - 2005 batch

7 years ago

Post Your Answer

Other Related Questions on Differential Calculus

Co-ordinates of the point on the curve x2+2xy+2y2=45 at which slope of tangent is -2,is/are ?(A) (3,0)(B)(-9,3)(C)(-3,1)(D)(9,-3)
Diifferentiating y w.r.t. x we get, 2x + 2(y+ xdy/dx) + 4ydy/dx = 0 dy/dx = -(x+y)/(x+2y) = -2 on solving, x + 3y = 0 or x = -3y put in the curve and solve we get y = + 3 and – 3 and x = -9 ...
2017 years ago
does limit of a function exist if its right hand limit exists but not left hand limit
Dear Student, for the limit of function to be exists, Both the Right hand and left hand limit should exists as well as they should be equal. Hence for the given case, limit will not exists....
Vijay Mukati 11 months ago
Dear Your Q. is not stiesfies the defnition of limit so that we can simply say that one sided limit exists only this can not imply the existence of the limit.
Kumar one month ago
Question: If xe^(xy) – y = sin^2x, then find dy/dx at x=0.
Given eqn. xe^(xy) – y = sin^2x, Differentiate y w.r.t. x as: (1)e^(xy) + xe^(xy)*[1.y + xdy/dx] – dy/dx = sin2x collect dy/dx, put x = 0: dy/dx = 1 is the answer.
Vikas TU 4 months ago
xe^xy – y = sin^2x ∴ y = xe^xy – sin^2x Differention both sides w.r.t x: dy/dx = (1).(e^xy) + (x).(ye^xy) – 2.sinx.cosx ∴ dy/dx = e^xy + xy.e^xy – 2.sinx.cosx NOTE: Differentiate xe^xy by...
Praneet Debnath 4 months ago
From any point on the line 2x + y = 1, tangents are drawn to the circle x^2 +y^2 = 9, then the chords of contact pass through a fixed point (A) (18, 9) (B) (9, 18) (C) (9,9) (D) (18,18)
Assume that point in parametric form on line 2x + y = 1 as: (x , 1-2x) and apply chords of contact concept here that is: T = 0. and put the point (x,1-2x). and try to satisfy the options...
Vikas TU 2 months ago
Why we consider speed as a scalar quantity, as while describing speed we know that an object is moving with a particular speed in some direction? It cannot happen that an object moving with ...
Scalar physical quantities are following physics laws and having magnitude ONLY.. Speed is just the rate of conversion of distance travelled, not associated with any concept of direction.....
Saurabh Kumar one year ago
hi Scalar physical quantities are following physics laws and having magnitude ONLY.. Speed is just the rate of conversion of distance travelled, not associated with any concept of...
Ankit Jaiswal 8 months ago
find all pairs of positive integers a,b such that a^b-b^a=3
Since RHS is odd, we must have either a is even and b is odd or vice versa. Case I: a is even, b is odd Also if , we must haveclearly, b>a. Hence and hence . (In fact looking modulo 3, a is ...
2017 years ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 400 off

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details