The value of displaystyle limx→0 (x3 cot x/1-cot x) is

Question

The value of displaystyle limx→0 (x3 cot x/1-cot x) is (A) 1 (B) -2 (C) 2 (D) 0

Tardigrade Admin · Accepted Answer

displaystyle limx→0 (x3 cot x/1-cot x) = displaystyle limx→ 0 ((x3 cot x/1-cot x)×(1+cot x/1-cot x)) = displaystyle limx→ 0((x/sin x))× displaystyle limx→ 0 cot x × displaystyle limx→ 0 (1+cot x) = 2

Q. The value of $x \to 0 lim \frac{x ^{3} co t x}{1 - co t x}$ is

1

-2

2

0

$x \to 0 lim \frac{x ^{3} co t x}{1 - co t x}$
$= x \to 0 lim (\frac{x ^{3} co t x}{1 - co t x} \times \frac{1 + co t x}{1 - co t x})$
$= x \to 0 lim (\frac{x}{s in x}) \times x \to 0 lim co t x \times x \to 0 lim (1 + co t x) = 2$

Q. The value of x→0lim​1−cotxx3cotx​ is

1

-2

2

0

x→0lim​1−cotxx3cotx​ =x→0lim​(1−cotxx3cotx​×1−cotx1+cotx​) =x→0lim​(sinxx​)×x→0lim​cotx×x→0lim​(1+cotx)=2

Q. The value of $x \to 0 lim \frac{x ^{3} co t x}{1 - co t x}$ is

$x \to 0 lim \frac{x ^{3} co t x}{1 - co t x}$
$= x \to 0 lim (\frac{x ^{3} co t x}{1 - co t x} \times \frac{1 + co t x}{1 - co t x})$
$= x \to 0 lim (\frac{x}{s in x}) \times x \to 0 lim co t x \times x \to 0 lim (1 + co t x) = 2$