Duration: 23:13

0 views

0

Consider 4 functions
\[
\begin{array}{l}
f(x)\left\{\begin{array}{cc}
x^{2} \sin \frac{1}{x}, & x \neq 0 \\
0, & x=0
\end{array}, g(x)=\left(x^{2}+1\right)|x+1|\right. \\
h(x)=\operatorname{sgn}\left(x^{2}-4 x+5\right) \text { and } k(x)=[\{x\}]
\end{array}
\]
A function is selected at random, three events are defined as \( A= \) selected function is continuous
\( B= \) selected function is derivable
\( C= \) derivative of selected function is continuous.
[Note: Where \( [y],\{y\} \) and \( \operatorname{sgn}(y) \) denotes greatest integer, fractional part and signum function of \( y \) respectively and \( P(E) \) represents probablility of event \( E] \)
(a) \( P\left(\frac{A}{B}\right)+P\left(\frac{B}{A}\right)=\frac{7}{4} \)
(b) \( P\left(\frac{A}{\bar{B}}\right)+P\left(\frac{B}{\bar{A}}\right)=1 \)
(c) \( P(A)+P(B)+P(C)=1 \)
(d) \( P(A)+P(B)+P(C)=\frac{9}{4} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live