#### Answer

The statement “I obtained $f'\left( x \right)$ by finding $\underset{h\to 0}{\mathop{\lim }}\,\left[ f\left( a+h \right)-f\left( a \right) \right]\text{ and }\underset{h\to 0}{\mathop{\lim }}\,h$ and then using the quotient rule for limits.” does not make sense.

#### Work Step by Step

The derivative of “f” at x is given by $f'\left( x \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( x+h \right)-f\left( x \right)}{h}$ provided this limit exists.
If the derivative $f'\left( x \right)$ is evaluated by finding $\underset{h\to 0}{\mathop{\lim }}\,\left[ f\left( a+h \right)-f\left( a \right) \right]\text{ and }\underset{h\to 0}{\mathop{\lim }}\,h$ and then using the quotient rule for limits, then the denominator will become $0$ and the value of $f'\left( x \right)$ will be undefined.
Thus, the statement does not make sense.