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

Evaluate the following limits:

`lim_(x -> 0) (sqrt(x^2 + "a"^2) - "a")/(sqrt(x^2 + "b"^2) - "b")`

Evaluate the following limits:

`lim_(x -> 0) (2 "arc"sinx)/(3x)`

Evaluate the following limits:

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

Evaluate the following limits:

`lim_(x -> 0) (tan 2x)/x`

Evaluate the following limits:

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

Evaluate the following limits:

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

Evaluate the following limits:

`lim_(x -> 0) (1 - cos^2x)/(x sin2x)`

Evaluate the following limits:

`lim_(x -> oo) x [3^(1/x) + 1 - cos(1/x) - "e"^(1/x)]`

Evaluate the following limits:

`lim_(x - oo){x[log(x + "a") - log(x)]}`

Evaluate the following limits:

`lim_(x -> pi) (sin3x)/(sin2x)`

Evaluate the following limits:

`lim_(x -> pi) (1 + sinx)^(2"cosec"x)`

Evaluate the following limits:

`lim_(x -> 0) (sqrt(2) - sqrt(1 + cosx))/(sin^2x)`

Evaluate the following limits:

`lim_(x -> 0) (sqrt(1 + sinx) - sqrt(1 - sinx))/tanx`

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`