7 For what value of K, F(X)= {tan3x/sin2x when x not equal to 0 and 2k when x = - Maths - Continuity and Differentiability

Question

7 For what value of K, F(X)= {tan3x/sin2x when x not equal to
0
and 2k when x = 0 is continuos for allx belongs to R?

ramandeep.singh · Accepted Answer

$f (x) = {\begin{matrix} \frac{\tan 3 x}{\sin 2 x}, x \neq 0 \\ 2 k, x = 0 \end{matrix}$

$\lim_{x \to 0^{+}} f (x) = \lim_{x \to 0^{+}} \frac{\tan 3 x}{\sin 2 x} = \lim_{x \to 0^{+}} (\frac{(\frac{\tan 3 x}{3 x})}{(\frac{\sin 2 x}{2 x})}) (\frac{3 x}{2 x}) = \lim_{x \to 0^{+}} \frac{1}{1} (\frac{3}{2}) = \frac{3}{2} f (x) |_{x = 0} = 2 k ∴ 2 k = \frac{3}{2} \Rightarrow k = \frac{3}{4}$

7. For what value of K, F(X)= {tan3x/sin2x when x not equal to 0 and 2k when x = 0 is continuos for allx belongs to R?

7. For what value of K, F(X)= {tan3x/sin2x when x not equal to 0

and 2k when x = 0 is continuos for allx belongs to R?