[CBSE 2021 (Term-I)]
Download our app for free and get started
(D) 8
$
\begin{aligned}
\lim _{x \rightarrow 0} f(x) & =\lim _{x \rightarrow 0} \frac{e^{3 x}-e^{-5 x}}{x} \\
& =\lim _{x \rightarrow 0} \frac{\left(e^{3 x}-1\right)+\left(1-e^{-5 x}\right)}{x} \\
& =\lim _{x \rightarrow 0} \frac{e^{3 x}-1}{x}-\lim _{x \rightarrow 0} \frac{e^{-5 x}-1}{x} \\
& =\lim _{3 x \rightarrow 0} \frac{e^{3 x}-1}{3 x} \cdot 3-\lim _{-5 x \rightarrow 0} \frac{e^{-5 x}-1}{-5 x} \cdot(-5) \\
& =(1)(3)-(1)(-5) \\
& =3+5=8
\end{aligned}
$
$x=0$, पर सांतत्य के लिए
$
\lim _{x \rightarrow 0} f(x)=f(0)
$
$\begin{array}{ll}\Rightarrow & 8=k \\ \therefore & k=8\end{array}$
$
\begin{aligned}
\lim _{x \rightarrow 0} f(x) & =\lim _{x \rightarrow 0} \frac{e^{3 x}-e^{-5 x}}{x} \\
& =\lim _{x \rightarrow 0} \frac{\left(e^{3 x}-1\right)+\left(1-e^{-5 x}\right)}{x} \\
& =\lim _{x \rightarrow 0} \frac{e^{3 x}-1}{x}-\lim _{x \rightarrow 0} \frac{e^{-5 x}-1}{x} \\
& =\lim _{3 x \rightarrow 0} \frac{e^{3 x}-1}{3 x} \cdot 3-\lim _{-5 x \rightarrow 0} \frac{e^{-5 x}-1}{-5 x} \cdot(-5) \\
& =(1)(3)-(1)(-5) \\
& =3+5=8
\end{aligned}
$
$x=0$, पर सांतत्य के लिए
$
\lim _{x \rightarrow 0} f(x)=f(0)
$
$\begin{array}{ll}\Rightarrow & 8=k \\ \therefore & k=8\end{array}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1यदि $2 x+8 y=\sin x$, तो $\frac{d y}{d x}$ है-View Solution
- 2$\cos ^{-1}\left(4 x^3-3 x\right)$ का अवकलज है$-$View Solution
- 3$e^{2 x}$ का $e^x$ के सापेक्ष अवकलज है-View Solution
- 4$\log \left[\log \left(\log x^5\right)\right]$ का $x$ के सापेक्ष अवकलन है-View Solution
- 5यदि $\sin y=x \cos (a+y)$, तब $\frac{d x}{d y}$ है-View Solution
- 6यदि फलन $f(x)=\left\{\begin{array}{c}\frac{x^2-16}{x-4}, x \neq 4 \\ k, x=4\end{array}, x=4\right.$ पर संतत है, तो $k$ का मान है-View Solution
- 7K के किस मान के लिए निम्न फलन $x =1$ पर सतत् हैView Solution
$f ( x )=\left\{\begin{array}{cc}\frac{x^2-3 x+2}{x-1} & , \quad x \neq 1 \\ k & , \quad x=1\end{array}\right.$ - 8यदि $3 x +2 y =\sin x$, तो $\frac{d y}{d x}$ है -View Solution
- 9View Solution
- 10यदि $x - y =\pi$ तो $\frac{d y}{d x}$ का मान होगा -View Solution