Question

The function f(x) $\frac{5^{n + 1} + 3^{n} - 3^{2n}}{5^{n} + 2^{n} + 3^{2n + 3}}$ is continuous at x = 0 if

• A. a = 0
• B. a = 3/5
• C. a = 2
• D. a = $\lim_{x \rightarrow 0}\frac{f(x^{2}) - f(x)}{f(x) - f(0)}$

Answer 1

Answer: (B)

a = 3/5

Answer 2

$\operatorname { l } _ { x \rightarrow 0 } \left[ \frac { \sin x ^ { 1 / 3 } } { x ^ { 1 / 3 } } \times \frac { \log ( 1 + 3 x ) } { 3 x } \times \left( \frac { \sqrt { x } } { \tan ^ { - 1 } \sqrt { x } } \right) ^ { 2 } \times \frac { 5 \cdot \sqrt [ 3 ] { x } } { e ^ { 5 \cdot \sqrt [ 3 ] { x } } - 1 } \times \frac { 3 } { 5 } \right]$

= 1 × 1 × (1)² × $\frac { 3 } { 5 }$×1 = $\frac { 3 } { 5 }$