Question

f $\lim _ { x \rightarrow 0 }$ $\frac{a^{x} - a^{- x}}{2}$, a, b, c ∈ R – {0}, exists and non-zero, then-

• A. a – b + c = 0
• B. a – b – c = 0
• C. a + b – c = 0
• D. None of these

Answer 1

Answer: (C)

a + b – c = 0

Answer 2

$\lim _ { x \rightarrow 0 }$ $\frac { x ^ { a } \left( \frac { \sin x } { x } \right) ^ { b } \cdot x ^ { b } } { \left( \frac { \sin x ^ { c } } { x ^ { c } } \right) \cdot x ^ { c } }$

$\lim _ { x \rightarrow 0 }$ x^{a + b – c}

For non zero value a + b – c = 0