If f(x) = lim_{n rightarrow infty} left( frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We analyze the limit $f(x) = \lim_{n \rightarrow \infty} \frac{\log(2+x) - x^{2n} \sin x}{1+x^{2n}}$.Case $1$: If $0 \leq x < 1$, then $x^{2n} \ri

Vedclass · Accepted Answer

discontinuous

Vedclass · Answer

(B) We analyze the limit $f(x) = \lim_{n ightarrow \infty} \frac{\log(2+x) - x^{2n} \sin x}{1+x^{2n}}$.Case $1$: If $0 \leq x Case $2$: If $x = 1$, then $f(1) = \lim_{n ightarrow \infty} \frac{\log(3) - 1^{2n} \sin(1)}{1+1^{2n}} = \frac{\log 3 - \sin 1}{2}$.Case $3$: If $1 Now, check continuity at $x=1$:Left-hand limit: $\lim_{x ightarrow 1^-} f(x) = \log(2+1) = \log 3$.Right-hand limit: $\lim_{x ightarrow 1^+} f(x) = -\sin(1)$.Since $\log 3 
eq -\sin 1$, the function is discontinuous at $x=1$.

If $f(x) = \lim_{n \rightarrow \infty} \left( \frac{\log(2+x) - x^{2n} \sin x}{1+x^{2n}} \right)$ for $0 \leq x \leq \frac{\pi}{2}$, then at $x=1$, $f(x)$ is

Similar Questions

If $f(x) = \begin{cases} Kx^2, & x \leq 2 \\ 3, & x > 2 \end{cases}$ is continuous at $x = 2$,then the value of $K$ is:

If $f(x) = \begin{cases} 2^{1/x}, & x \ne 0 \\ 3, & x = 0 \end{cases}$,then:

Let $f(x) = \frac{1 - \tan x}{4x - \pi }, x \ne \frac{\pi }{4}, x \in [0, \frac{\pi }{2}]$. If $f(x)$ is continuous in $[0, \frac{\pi }{2}]$,then $f(\frac{\pi }{4})$ is

In order that the function $f(x) = (x + 1)^{1/x}$ is continuous at $x = 0$,$f(0)$ must be defined as

Let $f: R \to R$ be a function defined by $f(x) = [x] \cos \left( \frac{2x - 1}{2} \pi \right)$,where $[x]$ denotes the greatest integer function. Then $f$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module