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

Evaluate : `lim_(x -> 3) (x^2 - 9)/(x - 3)` if it exists by finding `f(3^-)` and `f(3^+)`

Verify the existence of `lim_(x -> 1) f(x)`, where `f(x) = {{:((|x - 1|)/(x - 1)",",  "for"  x ≠ 1),(0",",  "for"  x = 1):}`

Evaluate the following limits:

`lim_(x -> 2) (x^4 - 16)/(x - 2)`

Evaluate the following limits:

`lim_(x ->) (x^"m" - 1)/(x^"n" - 1)`, m and n are integers

Evaluate the following limits:

`lim_(sqrt(x) -> 3) (x^2 - 81)/(sqrt(x) - 3)`

Evaluate the following limits:

`lim_("h" -> 0) (sqrt(x + "h") - sqrt(x))/"h", x > 0`

Evaluate the following limits:

`lim_(x -> 5) (sqrt(x + 4) - 3)/(x - 5)`

Evaluate the following limits:

`lim_(x -> 2) (1/x - 1/2)/(x - 2)`

Evaluate the following limits:

`lim_(x -> 1) (sqrt(x) - x^2)/(1 - sqrt(x))`

Evaluate the following limits:

`lim_(x -> 0) (sqrt(x^2 + 1) - 1)/(sqrt(x^2 + 16) - 4)`

Evaluate the following limits:

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

Evaluate the following limits:

`lim_(x -> 1) (root(3)(7 + x^3) - sqrt(3 + x^2))/(x - 1)`

Evaluate the following limits:

`lim_(x -> 2) (2 - sqrt(x + 2))/(root(3)(2) - root(3)(4 - x))`

Evaluate the following limits:

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

Evaluate the following limits:

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

Evaluate the following limits:

`lim_(x -> 5) (sqrt(x - 1) - 2)/(x - 5)`

Evaluate the following limits:

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

Find the left and right limits of f(x) = `(x^2 - 4)/((x^2 + 4x+ 4)(x + 3))` at x = – 2

Find the left and right limits of f(x) = tan x at x = `pi/2`

Evaluate the following limits:

`lim_(x -> 3) (x^2 - 9)/(x^2(x^2 - 6x + 9))`