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

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

Evaluate `lim_(x -> 0) (sqrt(2 + x) - sqrt(2))/x`

Find the positive integer n so that `lim_(x -> 3) (x^n - 3^n)/(x - 3)` = 108.

Evaluate `lim_(x -> pi/2) (secx - tanx)`

Evaluate `lim_(x -> 0)  (sin(2 + x) - sin(2 - x))/x`

Evaluate `lim_(x -> pi/6) (2sin^2x + sin x - 1)/(2sin^2 x - 3sin x + 1)`

Evaluate `lim_(x -> 0) (tanx - sinx)/(sin^3x)`

Evaluate `lim_(x -> a) (sqrt(a + 2x) - sqrt(3x))/(sqrt(3a + x) - 2sqrt(x))`

Evaluate `lim_(x -> 0) (cos ax - cos bx)/(cos cx - 1)`

Find the derivative of f(x) = `sqrt(sinx)`, by first principle.

`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)`