Arts (English Medium) Class 11 - CBSE Question Bank Solutions

`lim_(x -> 0) sinx/(x(1 + cos x))` is equal to ______.

`lim_(x -> pi/2) (1 - sin x)/cosx` is equal to ______.

`lim_(x -> 0) |x|/x` is equal to ______.

`lim_(x -> 1) [x - 1]`, where [.] is greatest integer function, is equal to ______.

If f(x) = x sinx, then f" `pi/2` is equal to ______.

Evaluate: `lim_(x -> 3) (x^2 - 9)/(x - 3)`

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

Evaluate: `lim_(x -> 0) ((x + 2)^(1/3) - 2^(1/3))/x`

Evaluate: `lim_(x -> a) ((2 + x)^(5/2) - (a + 2)^(5/2))/(x - a)`

Evaluate: `lim_(x -> 1) (x^4 - sqrt(x))/(sqrt(x) - 1)`

Evaluate: `lim_(x -> sqrt(2)) (x^4 - 4)/(x^2 + 3sqrt(2x) - 8)`

Evaluate: `lim_(x -> 1) (x^7 - 2x^5 + 1)/(x^3 - 3x^2 + 2)`

Evaluate: `lim_(x -> 0) (sqrt(1 + x^3) - sqrt(1 - x^3))/x^2`

Evaluate: `lim_(x -> 3) (x^3 + 27)/(x^5 + 243)`

Evaluate: `lim_(x -> 1/2) (8x - 3)/(2x - 1) - (4x^2 + 1)/(4x^2 - 1)`

Evaluate: `lim_(x -> 0) (sin 3x)/(sin 7x)`

Evaluate: `lim_(x -> 0) (sin^2 2x)/(sin^2 4x)`

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

Evaluate: `lim_(x -> 0) (2 sin x - sin 2x)/x^3`

Evaluate: `lim_(x -> 0) (1 - cos mx)/(1 - cos nx)`