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

Evaluate the following limits:

`lim_(x -> oo) ((2x^2 + 3)/(2x^2 + 5))^(8x^2 + 3)`

Evaluate the following limits:

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

Evaluate the following limits:

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

Evaluate the following limits:

`lim_(x -> 0) (sinalphax)/(sinbetax)`

Evaluate the following limits:

`lim_(x -> 0) (tan 2x)/(sin 5x)`

Evaluate the following limits:

`lim_(alpha -> 0) (sin(alpha^"n"))/(sin alpha)^"m"`

Evaluate the following limits:

`lim_(x -> 0) (sin("a" + x) - sin("a" - x))/x`

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`