If f x - left begin matrix k- -when - X -0lendmatrix right is continuous at x -0- then the value of k will beA- 1 B- 2-5C- -2-5D- None of these

The correct option is B 2/5lim_x → 0f(x)=lim_x → 02 sin 2x/2x.5=2/5=k ...

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Byju's Answer

Standard XII

Mathematics

Expansions to Remove Indeterminate Form

If f x = left...

Question

If $f (x) = {\begin{matrix} \frac{s i n 2 x}{5 x}, & w h e n x \neq 0 k, & w h e n x = 0 \end{matrix}$ is continuous at x = 0, then the value of k will be

1

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\frac{2}{5}

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- \frac{2}{5}

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N o n e o f t h e s e

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Solution

The correct option is B $\frac{2}{5}$
${lim}_{x \to 0} f (x) = {lim}_{x \to 0} \frac{2 s i n 2 x}{2 x .5} = \frac{2}{5} = k$

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If f(x)={sin2x5x,when x≠0k,when x=0 is continuous at x = 0, then the value of k will be

The correct option is B 25limx→0f(x)=limx→02 sin2x2x.5=25=k

If $f (x) = {\begin{matrix} \frac{s i n 2 x}{5 x}, & w h e n x \neq 0 k, & w h e n x = 0 \end{matrix}$ is continuous at x = 0, then the value of k will be

The correct option is B $\frac{2}{5}$
${lim}_{x \to 0} f (x) = {lim}_{x \to 0} \frac{2 s i n 2 x}{2 x .5} = \frac{2}{5} = k$