If f(x) = begin{cases} sin x, & x neq npi, n | vedclass

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

Question

(D) We need to evaluate $\lim_{x ightarrow 0} g(f(x))$.As $x ightarrow 0$,$x 
eq n\pi$ for $n 
eq 0$. Thus,$f(x) = \sin x$.As $x ightarrow 0$,

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) We need to evaluate $\lim_{x ightarrow 0} g(f(x))$.As $x ightarrow 0$,$x 
eq n\pi$ for $n 
eq 0$. Thus,$f(x) = \sin x$.As $x ightarrow 0$,$f(x) = \sin x ightarrow 0$.Since $f(x) ightarrow 0$ but $f(x) 
eq 0$ for $x$ in a deleted neighborhood of $0$,we look at the definition of $g(u)$ as $u ightarrow 0$.For $u 
eq 0, 2$,$g(u) = u^2 + 1$.Therefore,$\lim_{u ightarrow 0} g(u) = \lim_{u ightarrow 0} (u^2 + 1) = 0^2 + 1 = 1$.Thus,$\lim_{x ightarrow 0} g(f(x)) = 1$.

If $f(x) = \begin{cases} \sin x, & x \neq n\pi, n \in I \\ 2, & \text{otherwise} \end{cases}$ and $g(x) = \begin{cases} x^2 + 1, & x \neq 0, 2 \\ 2, & x = 0 \\ 4, & x = 2 \end{cases}$,then find $\lim_{x \rightarrow 0} g(f(x))$.

Similar Questions

If $f(x)=3x-2$ and $g(x)=x^2$,then $f \circ g(x) = \_\_\_\_$

If $\phi(x) = x^2 + 1$ and $\psi(x) = 3^x$,then find $\phi \{ \psi(x) \}$ and $\psi \{ \phi(x) \}$.

If $f(x)=-|x|$,then $(f \circ f \circ f)(x) + (f \circ f \circ f)(-x) =$

Let $Q$ be the set of all rational numbers in $[0,1]$ and $f:[0,1] \rightarrow [0,1]$ be defined by $f(x) = \begin{cases} x & \text{for } x \in Q \\ 1-x & \text{for } x \notin Q \end{cases}$. Then,the set $S = \{x \in [0,1] : (f \circ f)(x) = x\}$ is equal to

If $g(x)=3x^{2}+2x-3,$ $f(0)=-3$ and $4g(f(x))=3x^{2}-32x+72,$ then $f(g(2))$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module