Let a - 0 be a real number- Then the limit limx- 2ax-a3-x-a2-aa3-x-ax-2 is

The correct option is D 2/3(1 a) lim_x→ 2a^x+a^3 x (a^2+a)a^3 x a^x/2 lim_x→ 2(a^x a)(a^x/2 a)(a^x/2+a)(a a^x/2)(a^2+a^x+a^x/2a) lim_x→ 2 ...

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Factorization Method Form to Remove Indeterminate Form

Let a > 0 be ...

Question

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

2 log a

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- \frac{4}{3} a

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\frac{a^{2} + a}{2}

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\frac{2}{3} (1 - a)

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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

lim x \to a \frac{x . \int_{a}^{x} f (x) d x}{x - a} = a^{3} + a^{2}

(a \neq 0)

f (2 a)

\lim_{x \to a} \frac{x^{2 / 3} - a^{2 / 3}}{x^{3 / 4} - a^{3 / 4}}

A_{1}, A_{2},

A_{3}

R^{2}

A_{1} = {(x, y) : x \geq 0, y \geq 0, 2 x + 2 y - x^{2} - y^{2} > 1 > x + y}, A_{2} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{2} + y^{2}}, A_{3} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{3} + y^{3}} .

| A_{1} |, | A_{2} |,

| A_{3} |

A_{1}, A_{2}

A_{3}

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