Lf f - R- R is defined by fx- cos 3x-cos x-x2 for x- 0- - for x-0 -and if f is continuous at x-0 then -

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lf f : R→...

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lf $f$ : $R \to R$ is defined by $f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{cos 3 x - cos x}{x^{2}} & f o r x \neq 0 λ & f o r x = 0 \end{matrix}$ and if $f$ is continuous at $x = 0$ then $λ =$

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f : R \to R

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{cos 3 x - cos x}{x^{2}} & , f o r x \neq 0 λ, & , f o r x = 0 \end{matrix} ⎫ ⎬ ⎭

f

x = 0

λ

f (x) = \{\begin{matrix} \frac{\cos 3 x - \cos x}{x^{2}}, & x \neq 0 \\ λ, & x = 0 \end{matrix}

f (x) = \{\begin{matrix} 3 x - 2, & x < 0; \\ 1, & x = 0; \\ 4 x + 1, & x > 0 . \end{matrix}

f

R / {0} \to R

f (x) = \frac{1}{x} - \frac{2}{e^{2 x} - 1}

x = 0

f (0)

f : R \to R

f (x) = 2 x + 5

x > 0; f (x) = 3 x - 2

x \leq 0 :

f

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