Evaluate the limit- limx- 02x-sinx tanx-x

We have, lim_x→ 02x sinx tanx+x It becomes 0/0 form. =lim_x→ 0x(2 sinxx)x( tanxx+1) =lim_x→ 0(2 sinxx)( tanxx+1) nbsp;[∵lim_x→ 0sinxx = 1, lim_x→ 0tanxx = ...

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Standard XII

Mathematics

Derivative of Standard Functions

Evaluate the ...

Question

Evaluate the limit:

$lim x \to 0 \frac{2 x - s i n x}{t a n x + x}$

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Solution

We have,

$lim x \to 0 \frac{2 x - s i n x}{t a n x + x}$

It becomes 0/0 form.

$= lim x \to 0 \frac{x (2 - \frac{s i n x}{x})}{x (\frac{t a n x}{x} + 1)}$

$= lim x \to 0 \frac{(2 - \frac{s i n x}{x})}{(\frac{t a n x}{x} + 1)}$

$[∵ lim x \to 0 \frac{s i n x}{x} = 1, lim x \to 0 \frac{t a n x}{x} = 1]$

$= \frac{2 - 1}{1 + 1}$

$= \frac{1}{2}$

Therefore,

$lim x \to 0 \frac{2 x - s i n x}{t a n x + x} = \frac{1}{2}$

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Derivative of Standard Functions

Standard XII Mathematics

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Evaluate the limit: limx→02x−sinxtanx+x

We have, limx→02x−sinxtanx+x It becomes 0/0 form. =limx→0x(2−sinxx)x(tanxx+1) =limx→0(2−sinxx)(tanxx+1) [∵limx→0sinxx=1,limx→0tanxx=1] =2−11+1 =12 Therefore, limx→02x−sinxtanx+x=12

Evaluate the limit:

$lim x \to 0 \frac{2 x - s i n x}{t a n x + x}$