If fx - tan xx - - then limx - fx -

Consider the given function. #10; #10; f( x )=tan xx π #10; #10; #160; #10; #10;Since, x→πlim f( x #10;) #10; #10; #160; #10; ...

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Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

If fx = tan...

Question

If $f (x) = \frac{tan x}{x - π}$ then $lim x \to π f (x) =$

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Solution

Consider the given function.

$f (x) = \frac{tan x}{x - π}$

Since, ${lim}_{x \to π} f (x)$

Thus,

${lim}_{x \to π} (\frac{tan x}{x - π})$

This is the $\frac{0}{0}$ form.

So, apply L-Hospital rule,

${lim}_{x \to π} (\frac{{sec}^{2} x}{1 - 0})$

${lim}_{x \to π} ({sec}^{2} x)$

$= {(sec π)}^{2}$

$= {(- 1)}^{2}$

$= 1$

Hence, this is the answer.

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If f(x)=tanxx−π then limx→πf(x)=

Consider the given function. f(x)=tanxx−π Since, limx→πf(x) Thus, limx→π(tanxx−π) This is the 00 form. So, apply L-Hospital rule, limx→π(sec2x1−0) limx→π(sec2x) =(secπ)2 =(−1)2 =1 Hence, this is the answer.

If $f (x) = \frac{tan x}{x - π}$ then $lim x \to π f (x) =$