Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Choose the correct answer out of 4 options given against each Question Let f(x) = x – [x], is A. 3/2 B. 1 C. 0 D. –1

Choose the correct answer out of 4 options given against each Question

Let f(x) = x – [x], \in \mathrm{R}, \text { then } \mathrm{f}^{\prime} \frac{1}{2}  is
A. 3/2
B. 1
C. 0
D. –1

Answers (1)

   \\ LHD=\mathop{\lim }_{h \rightarrow 0}\frac{ \left( f \left( \frac{1}{2}-h \right) -f \left( \frac{1}{2} \right) \right) }{-h} \\ \\ =\mathop{\lim }_{h \rightarrow 0}\frac{ \left( \left( \frac{1}{2}-h \right) - \left[ \left( \frac{1}{2}-h \right) \right] - \left( \frac{1}{2} \right) + \left[ \frac{1}{2} \right] \right) }{-h}=\mathop{\lim }_{h \rightarrow 0}\frac{-h}{-h}=1 \\ \\ RHD=\mathop{\lim }_{h \rightarrow 0}\frac{ \left( f \left( \frac{1}{2}+h \right) -f \left( \frac{1}{2} \right) \right) }{h} \\ \\ =\mathop{\lim }_{h \rightarrow 0}\frac{ \left( \left( \frac{1}{2}+h \right) - \left[ \left( \frac{1}{2}+h \right) \right] - \left( \frac{1}{2} \right) + \left[ \frac{1}{2} \right] \right) }{h}=\mathop{\lim }_{h \rightarrow 0}\frac{h}{h}=1 \\ \\

 Hence, the answer is option B

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question