HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Evaluate the following limits:

`lim_(x -> oo) ((x^2 - 2x + 1)/(x^2 -4x + 2))^x`

Evaluate the following limits:

`lim_(x -> 0) ("e"^x - "e"^(-x))/sinx`

Evaluate the following limits:

`lim_(x -> 0) ("e"^("a"x) - "e"^("b"x))/x`

Evaluate the following limits:

`lim_(x -> ) (sinx(1 - cosx))/x^3`

Evaluate the following limits:

`lim_(x -> 0) (tan x - sin x)/x^3`

Choose the correct alternative:

`lim_(x -> oo) sinx/x`

Choose the correct alternative:

`lim_(x - pi/2) (2x - pi)/cos x`

Choose the correct alternative:

`lim_(x -> 0) sqrt(1 - cos 2x)/x`

Choose the correct alternative:

`lim_(theta -> 0) (sinsqrt(theta))/(sqrt(sin theta)`

Choose the correct alternative:

`lim_(x -> oo) ((x^2 + 5x + 3)/(x^2 + x + 3))^x` is

Choose the correct alternative:

`lim_(x - oo) sqrt(x^2 - 1)/(2x + 1)` =

Choose the correct alternative:

`lim_(x -> 0) ("a"^x - "b"^x)/x` =

Choose the correct alternative:

`lim_(x -> 0) (8^x - 4x - 2^x + 1^x)/x^2` =

Choose the correct alternative:

If `f(x) = x(- 1)^([1/x])`, x ≤ 0, then the value of `lim_(x -> 0) f(x)` is equal to

Choose the correct alternative:

`lim_(x -> 3) [x]` =

Choose the correct alternative:

`lim_(x -> 0) (x"e"^x - sin x)/x` is

Choose the correct alternative:

If `lim_(x -> 0) (sin "p"x)/(tan 3x)` = 4, then the value of p is

Choose the correct alternative:

`lim_(alpha - pi/4) (sin alpha - cos alpha)/(alpha - pi/4)` is

Choose the correct alternative:

`lim_(x -> oo) (1/"n"^2 + 2/"n"^2 + 3/"n"^2 + ... + "n"/"n"^2)` is

Choose the correct alternative:

`lim_(x -> 0) ("e"^(sin x) - 1)/x` =