Question

$\underset{\mathbf{x}\mathbf{\rightarrow}\mathbf{a}}{\mathbf{\lim}}\frac{\mathbf{x}^{\mathbf{3}}\mathbf{-}\mathbf{a}^{\mathbf{3}}}{\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{a}^{\mathbf{2}}}\mathbf{=}$

• A. 0
• B. Not defined
• C. 2a
• D. $\frac{3a}{2}$

Answer 1

Answer: (D)

$\frac{3a}{2}$

Answer 2

$\lim _ { x \rightarrow a } \frac { x ^ { 3 } - a ^ { 3 } } { x ^ { 2 } - a ^ { 2 } }$ $\left( \frac{0}{0}\text{form} \right)$ = $\lim_{x \rightarrow a}\frac{3x^{2}}{2x}$ (By ‘L’ Hospital rule)

= $\frac{3a^{2}}{2a} = \frac{3a}{2}$.