Let a -0 be a real number- Then the limit lim x - 2ax-a3-x-a2-a-a3-x-ax-2 isA- 2 log aB- -4-3 aC- a2-a-2D- 2-31-a

The correct option is D x → 2lima^x + a^3 x (a^2+a)/a^3 x a^x/2 x → 2lim(a^x a)(a^x/2 a)(a^x/2+a)/(a a^x/2)(a^2+a^x + a^x/2.a) x → 2lim (a^x a)(a^x/2+a)/a ...

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Byju's Answer

Standard XII

Mathematics

Second Fundamental Theorem of Calculus

Let a >0 be a...

Question

Let a > 0 be a real number. Then the limit $l i m x \to 2 \frac{a^{x} + a^{3 - x} - (a^{2} + a)}{a^{3 - x} - a^{\frac{x}{2}}}$ is

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Solution

The correct option is D

$l i m x \to 2 \frac{a^{x} + a^{3 - x} - (a^{2} + a)}{a^{3 - x} - a^{\frac{x}{2}}} l i m x \to 2 \frac{(a^{x} - a) (a^{\frac{x}{2}} - a) (a^{\frac{x}{2}} + a)}{(a - a^{\frac{x}{2}}) (a^{2} + a^{x} + a^{\frac{x}{2}} . a)} l i m x \to 2 - \frac{(a^{x} - a) (a^{\frac{x}{2}} + a)}{a^{2} + a^{x} + a^{\frac{x}{2}} . a} = \frac{2}{3} (1 - a)$

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Let a > 0 be a real number. Then the limit limx→2ax+a3−x−(a2+a)a3−x−ax2 is

The correct option is D limx→2ax+a3−x−(a2+a)a3−x−ax2limx→2(ax−a)(ax2−a)(ax2+a)(a−ax2)(a2+ax+ax2.a)limx→2−(ax−a)(ax2+a)a2+ax+ax2.a=23(1−a)

Let a > 0 be a real number. Then the limit $l i m x \to 2 \frac{a^{x} + a^{3 - x} - (a^{2} + a)}{a^{3 - x} - a^{\frac{x}{2}}}$ is