Question

Xcosx + sinx / x^2+ tanx lim x0

Answer 1

Step-by-step explanation:

We have,

$\displaystyle\lim_{x \to0} \dfrac{x \cos(x) + \sin(x) }{ {x}^{2} + \tan(x) }$

$\displaystyle = \lim_{x \to0} \dfrac{x \cos(x) + \sin(x) }{x \left \{ x + \dfrac{\tan(x) }{x} \right \}}$

$\displaystyle = \lim_{x \to0} \dfrac{ \cos(x) + \dfrac{ \sin(x)}{x} }{ x + \dfrac{\tan(x) }{x} }$

$= \dfrac{ \displaystyle \lim_{x \to0} \left \{ \cos(x) + \dfrac{ \sin(x)}{x} \right \}}{ \displaystyle \lim_{x \to0} \left \{ x + \dfrac{\tan(x) }{x} \right \}}$

$= \dfrac{ \displaystyle \lim_{x \to0} \cos(x) + \lim_{x \to0} \dfrac{ \sin(x)}{x} }{ \displaystyle \lim_{x \to0} x + \lim_{x \to0} \dfrac{\tan(x) }{x} }$

$= \dfrac{ 1 + 1}{ 0 + 1 }$

$= \dfrac{ 2}{ 1 }$

$= 2$

Answer 2

Answer:

your solution is in above pic

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