Highly selective Backlog Qs for JEE MainMathematicsLimits

Let a>0 be a real number. Then the limit _ x 2 a^ x +a^ 3-x - (a²+a ) a^ 3-x -a^ x / 2 is

Options

A2 a
B- 4 3 a
Ca²+a 2
D2 3 (1-a)

Correct answer

D. 2 3 (1-a)

Step-by-step solution

_ x 2 a^ x +a^ 3-x - (a²+a ) a^ 3-x -a^ x / 2 _ x 2 (a^ x -a ) (a^ x / 2 -a ) (a^ x / 2 +a ) (a-a^ x / 2 ) (a²+a^ x +a^ x / 2 a ) _ x 2 - (a^ x -a ) (a^ x / 2 +a ) a²+a^ x +a^ x / 2 a = 2 3 (1-a)

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