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

Show that `lim_(x -> 4) |x - 4|/(x - 4)` does not exists

`lim_(x -> pi) sinx/(x - pi)` is equal to ______.

`lim_(x -> 0) (x^2 cosx)/(1 - cosx)` is ______.

`lim_(x -> 0) ((1 + x)^n - 1)/x` is equal to ______.

`lim_(x -> 1) (x^m - 1)/(x^n - 1)` is ______.

`lim_(x -> 0) (1 - cos 4theta)/(1 - cos 6theta)` is ______.

`lim_(x -> 0) ("cosec" x - cot x)/x` is equal to ______.

`lim_(x -> 0) sinx/(sqrt(x + 1) - sqrt(1 - x)` is ______.

`lim_(x -> pi/4) (sec^2x - 2)/(tan x - 1)` is equal to ______.

`lim_(x -> 1) ((sqrt(x) - 1)(2x - 3))/(2x^2 + x - 3)` is ______.

If `f(x) = {{:(sin[x]/[x]",", [x] ≠ 0),(0",", [x] = 0):}`, where [.] denotes the greatest integer function, then `lim_(x -> 0) f(x)` is equal to ______.

`lim_(x -> 0) |sinx|/x` is ______.

If `f(x) = {{:(x^2 - 1",", 0 < x < 2),(2x + 3",", 2 ≤ x < 3):}`, the quadratic equation whose roots are `lim_(x -> 2^-) f(x)` and `lim_(x -> 2^+) f(x)` is ______. 

`lim_(x -> 0) (tan 2x - x)/(3x - sin x)` is equal to ______.

If `f(x) = tanx/(x - pi)`, then `lim_(x -> pi) f(x)` = ______.

`lim_(x -> 0) (sin mx cot  x/sqrt(3))` = 2, then m = ______. 

`lim_(x -> 3^+) x/([x])` = ______.

Prove the following statement by contradication method.
p: The sum of an irrational number and a rational number is irrational.

What universal set (s) would you propose for the following:

The set of right triangles.

What universal set (s) would you propose for the following:

The set of isosceles triangles.