Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsLimits

lim x → 1 1 - cos 2 x - 1 x - 1

Options

  1. Aexists and it equal to 2
  2. Bexists and it equals - 2
  3. Cdoes not exist because x - 1 → 0
  4. Ddoes not exist because the left hand limit is not equal to the right hand limit

Correct answer

D. does not exist because the left hand limit is not equal to the right hand limit

Step-by-step solution

lim x → 1 1 - cos 2 x - 1 x - 1 = lim x → 1 2 sin x - 1 x - 1 But lim x → 1 + 2 sin x - 1 x - 1 = 2 lim x → 1 + sin x - 1 x - 1 = 2 and lim x → 1 – 2 sin x - 1 x - 1 = - 2 lim x → 1 - sin x - 1 x - 1 = - 2 .

Practice Limits on Quantrex Academy →

More from Limits

Let _ x 2 ( (x-2))(rx^2 + (p-2)x - 2p) (x-2)^2 = 5 for some r, p R . If the set of all possible values of q , such that the roots of the equation rx^2 - px + q = 0 lie in (0, 2) , 2026The value of _ x 0 ( x^2 ^2 x x^2 - ^2 x ) is: 2026Let f(x) = _ y 0 (1 - (xy)) (xy) y^3 . Then the number of solutions of the equation f(x) = x , x R is : 2026The product of all possible values of , for which _ x 0 ( 1 - ( x) (( +1)x) (( +2)x) ^2(( +1)x) ) = 2 , is: 2026If _ x 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to : 2026The value of _ x 0 _ e ( (e x) (e² x ) (e¹⁰ x ) ) e²-e^ 2 x is equal to 2026If _ x 0 e ^ ( a -1) x +2 ~b x+( c -2) e ^ -x x x- _ e (1+x) =2 , then a ²+ b ²+ c ² is equal to : 2026Let [ ] denote the greatest integer function and f(x)= _ n 1 n ³ _ k =1 ^ n [ k ² 3^ x ] . Then 12 _ j =1 ^ f( j ) is equal to _ _ _ _ . 2026 Full Limits list All 99 Percentile Qs Bank for JEE Main PYQs