79911 If \(f(x)=\left\{\begin{array}{cc}\frac{\log (1+2 a x)-\log (1-b x)}{x}, x \neq 0 \\ k, x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)

79912 If \(\begin{aligned} f(x) & =\frac{\left(e^{k x}-1\right)^2 \sin x}{x^3}, & & x \neq 0 \\ & =4, & & x=0\end{aligned}\)
\(f\) is continuous at \(x=0\), then \(k=\)

79913 If \(f(x)\) is continuous at \(x=0\), where
\(f(x)=\frac{\left(e^{3 x}-1\right) \cdot \sin x}{x^{2}} ;\) then, \(f(0)=\) ?

79914 The value of \(k\) if \(f(x)\) is continuous at \(x=\frac{\pi}{2}\), where
\(\begin{aligned} f(x) & =\frac{k \cos x}{\pi-2 x}, & & \text { for } & & x \neq \frac{\pi}{2} \\ & =3, & & \text { for } & & x=\frac{\pi}{2}\end{aligned}\) is

79911 If \(f(x)=\left\{\begin{array}{cc}\frac{\log (1+2 a x)-\log (1-b x)}{x}, x \neq 0 \\ k, x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)

79912 If \(\begin{aligned} f(x) & =\frac{\left(e^{k x}-1\right)^2 \sin x}{x^3}, & & x \neq 0 \\ & =4, & & x=0\end{aligned}\)
\(f\) is continuous at \(x=0\), then \(k=\)

79913 If \(f(x)\) is continuous at \(x=0\), where
\(f(x)=\frac{\left(e^{3 x}-1\right) \cdot \sin x}{x^{2}} ;\) then, \(f(0)=\) ?

79914 The value of \(k\) if \(f(x)\) is continuous at \(x=\frac{\pi}{2}\), where
\(\begin{aligned} f(x) & =\frac{k \cos x}{\pi-2 x}, & & \text { for } & & x \neq \frac{\pi}{2} \\ & =3, & & \text { for } & & x=\frac{\pi}{2}\end{aligned}\) is

79911 If \(f(x)=\left\{\begin{array}{cc}\frac{\log (1+2 a x)-\log (1-b x)}{x}, x \neq 0 \\ k, x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)

79912 If \(\begin{aligned} f(x) & =\frac{\left(e^{k x}-1\right)^2 \sin x}{x^3}, & & x \neq 0 \\ & =4, & & x=0\end{aligned}\)
\(f\) is continuous at \(x=0\), then \(k=\)

79913 If \(f(x)\) is continuous at \(x=0\), where
\(f(x)=\frac{\left(e^{3 x}-1\right) \cdot \sin x}{x^{2}} ;\) then, \(f(0)=\) ?

79914 The value of \(k\) if \(f(x)\) is continuous at \(x=\frac{\pi}{2}\), where
\(\begin{aligned} f(x) & =\frac{k \cos x}{\pi-2 x}, & & \text { for } & & x \neq \frac{\pi}{2} \\ & =3, & & \text { for } & & x=\frac{\pi}{2}\end{aligned}\) is

79911 If \(f(x)=\left\{\begin{array}{cc}\frac{\log (1+2 a x)-\log (1-b x)}{x}, x \neq 0 \\ k, x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)

79912 If \(\begin{aligned} f(x) & =\frac{\left(e^{k x}-1\right)^2 \sin x}{x^3}, & & x \neq 0 \\ & =4, & & x=0\end{aligned}\)
\(f\) is continuous at \(x=0\), then \(k=\)

79913 If \(f(x)\) is continuous at \(x=0\), where
\(f(x)=\frac{\left(e^{3 x}-1\right) \cdot \sin x}{x^{2}} ;\) then, \(f(0)=\) ?

79914 The value of \(k\) if \(f(x)\) is continuous at \(x=\frac{\pi}{2}\), where
\(\begin{aligned} f(x) & =\frac{k \cos x}{\pi-2 x}, & & \text { for } & & x \neq \frac{\pi}{2} \\ & =3, & & \text { for } & & x=\frac{\pi}{2}\end{aligned}\) is