If fx tan x x- then lim x - fx-

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Standard XII

Mathematics

Parametric Differentiation

If fx tan x x...

Question

If f(x) $\frac{\tan x}{x - π}, then \lim_{x \to π}$ f(x) = _____________________________.

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Solution

$Given f (x) = \frac{\tan x}{x - π} \begin{matrix} \begin{matrix} \lim \\ x \to π \end{matrix} \end{matrix} f (x) = \begin{matrix} \lim \\ x \to π \end{matrix} \frac{\tan x}{x - π} put x - π = h i . e . x = h + π where h \to 0 i . e . \begin{matrix} \lim \\ h \to 0 \end{matrix} \frac{\tan (π + h)}{h} i . e . \begin{matrix} \lim \\ h \to 0 \end{matrix} \frac{\tan h}{h} (∵ \tan (π + θ) = tanθ) = 1 (∵ \begin{matrix} \lim \\ θ \to 0 \end{matrix} \frac{tanθ}{θ} = 1) Hence, \begin{matrix} \lim \\ x \to π \end{matrix} f (x) = 1 .$

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If f(x) tan xx-π, then limx→π f(x) = _____________________________.

Given fx=tanxx-πlimx→π fx=limx→πtanxx-πput x-π=h i.e. x=h+π where h→0i.e. limh→0 tanπ+hhi.e. limh→0tanhh ∵ tanπ+θ=tanθ=1 ∵limθ→0tanθθ=1Hence, limx→πfx=1.

If f(x) $\frac{\tan x}{x - π}, then \lim_{x \to π}$ f(x) = _____________________________.