Question

Evaluate

${ \large{ \tt{{{ lim} \atop{x \rightarrow \: \frac{\pi}{4} } } \frac{ {cot}^{ 3} \theta \: - cot \: \theta}{cos(x + \frac{\pi}{4} )} }}}$
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Answer 1

Answer:

Lim x tends to π/4$[(tan^3x- tan x)/{cos (x+π/4)}]$. This is of the form 0/0. So by using l’Hopital’s rule we can write it as

Lim x tends to π/4$[{3tan^2 x.sec^2 x - sec^2 x}/{-sin(x+π/4)}$

=Limit x tends to π/4

$[{sec^2 x(3tan^2 x - 1)}/{- sin(x+π/4)}$

Now applying the limit

$[sec^2 (π/4){3tan^2 (π/4) - 1}/-sin(π/4+π/4)$

=2(3–1)/-1 =4/-1 = -4.

Answer 2

Answer:

$- 4 \: \: is \: the \: answer$