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The correct option is B 2 x→ 0Lim (sinx/x+cosx )=1+1=2 ...

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First Fundamental Theorem of Calculus

text I f∼ fx=...

Question

$If f (x) = {\begin{matrix} \frac{s i n x}{x} + c o s x, x \neq 0 k, x = 0 \end{matrix} is continuos at x = 0, t h e n k =$

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$If f (x) = {\begin{matrix} \frac{s i n x}{x}, & x \neq 0 1, & x = 0 \end{matrix}, then {lim}_{x \to 0} f (x) =$ is

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{e^{\frac{- x^{2}}{2}} - cos x}{x ln (1 + x) sin x (e^{x} - 1)}, & x \neq 0 k, & x = 0 \end{matrix} .

f (x)

x = 0

k

f (x) = {\begin{matrix} | x + 1 | & x \leq 0; x & x > 0; \end{matrix}

g (x) = {\begin{matrix} | x | + 2 & x < 2; - | x - 2 | & x \geq 2; \end{matrix}

f (x) - g (x)

If $f (x) = {\begin{matrix} x, & if w h e n x i s r a t i o n a l 0, & if w h e n x i s i r r a t i o n a l \end{matrix}$ ;

$g (x) = {\begin{matrix} 0, & if w h e n x i s r a t i o n a l x, & if w h e n x i s i r r a t i o n a l \end{matrix}$ ;

then $(f - g$ ) is

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