The value of displaystyle lim x arrow 0 ( cot 4 x/ textcosec 3 x) is equal to

Question

The value of displaystyle lim x arrow 0 ( cot 4 x/ textcosec 3 x) is equal to (A) (4/3) (B) (3/4) (C) (2/3) (D) (3/2)

Tardigrade Admin · Accepted Answer

Given, displaystyle lim x arrow 0 ( cot 4 x/ operatornamecosec 3 x) = displaystyle lim x arrow 0(( sin 3 x/ tan 4 x)) displaystyle lim x arrow 0 (( sin 3 x/3 x) × 3 x/( tan 4 x)4 x × 4 x) = displaystyle lim x arrow 0 (3 x/4 x)=(3/4)

Q. The value of $x \to 0 lim \frac{cot 4 x}{cosec 3 x}$ is equal to

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{3}{2}$

0

Given, $x \to 0 lim \frac{cot 4 x}{cosec 3 x}$
$= x \to 0 lim (\frac{sin 3 x}{tan 4 x})$
$x \to 0 lim \frac{\frac{s i n 3 x}{3 x} \times 3 x}{\frac{t a n 4 x}{4 x} \times 4 x}$
$= x \to 0 lim \frac{3 x}{4 x} = \frac{3}{4}$

Q. The value of x→0lim​cosec3xcot4x​ is equal to

34​

43​

32​

23​

0