Limits Continuity And Differentiability Question 56
If $ f(x)=x^{3} \cdot x, $ then
Options:
A) f is derivable at x=0
B) f is continuous but not derivable at x=0
C) LHD at x=0 is 1
D) RHD at x=0 is 1
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Answer:
Correct Answer: A
Solution:
We have $ f(x)= \begin{cases} x^{3},x>0 \\ 0,x=0 \\ -x^{2},x<0 \\ \end{cases} . $
Clearly, f(x) is continuous at x=0. (L.H.D. at x=0)=0 $ {{[ \frac{d}{dx}(-x^{3}) ]} _{x=0}}$=${{[-3x^{2}]} _{x=0}}=0 $
Similarly, (R.H.D. at x=0) =0. So, f(x) is continuous at x=0.
BETA
