NDA2016MathematicsLimitsActual
Consider the function f(x)= a ^ [x]+x -1 [x]+x where [ ] denotes the greatest integer function. What is _ x 0⁺ f(x) equal to?
Options
- A1
- Bln a
- C1- a ⁻¹
- DLimit does not exist
Correct answer
B. ln a
Step-by-step solution
Given f(x)= a^ [x]+x -1 [x]+x aligned _ x 0⁺ & f(x)= _ h 0 a^ [0+h]+(0+h) -1 [0+h]+(0+h) & = _ h 0 a^ [h]+(h) -1 [h]+h & = _ h 0 (a^h-1 ) h & = _e a aligned