Home
Class 12
MATHS
Let I (1) =lim (x to oo) sqrt((x-cos ^(2...

Let `I _(1) =lim _(x to oo) sqrt((x-cos ^(2)x)/(x+sin x))and l _(2) =lim _(h to 0^(+)) int _(-1) ^(1)(hdx)/(h ^(2)+ x ^(2))` Then:

A

Both `l _(1) and l _(2)` are less than 22/7

B

One of the two limits is rational and other irrational

C

`l _(2) gt l _(1)`

D

`l _(2)` is greater than 3 times of `l _(1)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos
  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|2 Videos
  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|29 Videos
  • HYPERBOLA

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos
  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

Let lim_(x->oo) sqrt((x-cos^2x)/(x+sinx)) and I_2 = lim_(h->0^+) int_(-1)^1 hdx/(h^2+x^2) . Then

lim_(x to 0) (1 - cos x)/(x sqrt(x^(2))

lim_(x to 0) (cos 2x-1)/(cos x-1)

Let f (x) =lim _(nto oo) tan ^(-1) (4n ^(2) (1- cos ""(pi)/(n )))and g (x) = lim _(n to oo) (n^(2))/(2) ln cos ((2x)/(n )) then lim _(xto0) (e ^(-2g (x))-ef (x))/(x ^(6)) equals.

Evaluate : lim_(x to oo) sqrt(x^(2)+x +1) - sqrt(x^(2)+1)

lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^(2)+1))

lim _(xrarr oo) (sqrt(x^2+x+1)-sqrt(x^2+1))=

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

If A=lim_(x to 0) (sin^(-1)(sinx))/(cos^(-1)(cosx))and B=lim_(x to 0)([|x|])/(x), then

lim_(x rarr oo)x{sqrt(x^(2)+1)-sqrt(x^(2)-1))}