Directions: (1 - 5) |
Let \[f\text{ }\left( x \right)\]be a real valued function, then its |
Left Hand Derivative (L.H.D.) : |
\[Lf'\left( a \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( a-h \right)-f\left( a \right)}{-h}\] |
Right Hand Derivative (R.H.D.) : |
\[Rf'\left( a \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( a+h \right)-f\left( a \right)}{h}\] |
Also, a function \[f\left( x \right)\]is said to be differentiable at x = a if its L.H.D. and R.H.D. at x = a exist and are equal. |
For the function answer the following questions |
A) 1
B) -1
C) 0
D) 2
Correct Answer: B
Solution :
We have, \[Rf'\left( 1 \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( 1+h \right)-f\left( 1 \right)}{h}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\,\frac{3-\left( 1+h \right)-2}{h}=\underset{h\to 0}{\mathop{\lim }}\,-\frac{h}{h}=-1\]You need to login to perform this action.
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