If \( f(x)=\lim _{n \rightarrow \infty} \frac{(1-\cos (1-\cos x))(x+1)^{n}+\lambda \sin \left(n-...
If \( f(x)=\lim _{n \rightarrow \infty} \frac{(1-\cos (1-\cos x))(x+1)^{n}+\lambda \sin \left(n-\sqrt{n^{2}-n}\right) x}{x^{4}(x+1)^{n}+x} \), \( x \neq 0 \) is continuous at \( x=0 \), then find the value of \( \lambda \)
(a) \( 1 / 2 \)
(b) \( -1 / 4 \)
(c) \( 1 / 4 \)
(d) \( 1 / 3 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-08 | If \( f(x)=\left\{\begin{array}{cc}\sin x, & x \neq n \pi, n=0, \pm 1, \pm 2, \ldots \ldots \\ 2... |
| 2023-06-08 | Which of the following limits does not exist?
(a) \( \lim _{x \rightarrow \infty} \operatorname{... |
| 2023-06-08 | \( f(x)=\left\{\begin{array}{l}x+\frac{1}{2}, x0 \\ 2 x+\frac{1}{3}, x \geq 0\end{array}\right. ... |
| 2023-06-08 | Let \( P_{n}=a^{P_{n-1}}-1, \forall n=2,3, \ldots \ldots \) and Let \( P_{1}=a^{x}-1 \) where \(... |
| 2023-06-08 | \[
\lim _{x \rightarrow \infty}\left(\sqrt{4 x^{2}+x}-\sqrt{\frac{4 x^{3}}{x+2}}\right)
\]
(a) \... |
| 2023-06-08 | Refer to the figure, the value of \( \lim _{x \rightarrow 0^{+}} \frac{f(-x) x^{2}}{\left\{\frac... |
| 2023-06-08 | \( \lim _{x \rightarrow 0} \frac{\sin x-x^{2}-\{x\} \cdot\{-x\}}{x \cos x-x^{2}-\{x\} \cdot\{-x\... |
| 2023-06-08 | The value of \( \lim _{x \rightarrow 1} \frac{\sqrt[3]{x}+\sqrt{x}+x \sqrt{x}-3}{x^{3}-1} \) is
... |
| 2023-06-08 | \( \lim _{x \rightarrow 0}\left\{(1+x)^{\frac{2}{x}}\right\} \) (where \( \{\cdot\} \) denotes t... |
| 2023-06-08 | \( \lim _{x \rightarrow \infty} \frac{\cos ^{-1}\left(x^{-a} \log _{a} x\right)}{\sec ^{-1}\left... |
| 2023-06-08 | If \( f(x)=\lim _{n \rightarrow \infty} \frac{(1-\cos (1-\cos x))(x+1)^{n}+\lambda \sin \left(n-... |
| 2023-06-08 | Let \( S_{n}=1+2+3+\ldots+n \) and \( P_{n}=\prod_{r=2}^{n} \frac{S_{r}}{S_{r}-1} \), where \( n... |
| 2023-06-08 | \[
\lim _{x \rightarrow \infty}\left(\frac{e^{\pi / x}+e^{-\pi / x}}{\cos (\pi / x)}\right)^{x^{... |
| 2023-06-08 | \[
\lim _{x \rightarrow \infty} x^{2} \sin \left(\ln \sqrt{\cos \frac{\pi}{x}}\right)
\]
(a) \( ... |
| 2023-06-08 | If \( \lim _{x \rightarrow \infty} x\left(\tan ^{-1}\left(\frac{x+\lambda}{x+\mu}\right)-\frac{\... |
| 2023-06-08 | If \( \lim _{x \rightarrow 0} \frac{a x-\sin 3 x}{x^{3}}=b \) and \( (a, b) \neq(0,0) \) then \(... |
| 2023-06-08 | The value of \( \lim _{x \rightarrow \pi^{-}} \frac{2^{\cot x}+3^{\cot x}-5^{1+\cot x}+2}{\left(... |
| 2023-06-08 | \( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\f... |
| 2023-06-08 | Let \( f(x)=\left\{\begin{array}{ll}x-[x] ; & x \notin I \\ 1 ; & x \in I\end{array} ;\right. \)... |
| 2023-06-08 | If \( \lim _{x \rightarrow 0} \frac{\sin (\sin x)-\sin x}{a x^{5}+b x^{4}+c x^{3}+d x^{2}}=-\fra... |
| 2023-06-08 | If \( \alpha \) and \( \beta \) are roots of \( x^{2}+\sqrt{1-\cos 2 \theta} x+\theta=0 \) where... |
0