Lim x- a - a-2x - 3a - x - a

The correct option is D =12√(3) Consider the following differential eq. #10; #10; x→ alim √(a+2x) √(3a)√(x) √(a) #10; #10; #10; #160; # ...

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Byju's Answer

Standard IX

Mathematics

Multiplication of Surds

lim x→ a √ a+...

Question

$lim x \to a \frac{\sqrt{a + 2 x} - \sqrt{3 a}}{\sqrt{x} - \sqrt{a}}$

= \frac{1}{3 \sqrt{3}}

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= \frac{1}{5 \sqrt{3}}

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= \frac{1}{7 \sqrt{3}}

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= \frac{1}{2 \sqrt{3}}

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Solution

The correct option is D $= \frac{1}{2 \sqrt{3}}$
Consider the following differential eq.

${lim}_{x \to a} \frac{\sqrt{a + 2 x} - \sqrt{3 a}}{\sqrt{x} - \sqrt{a}}$

Using the L- Hospital rules,

$= {lim}_{x \to a} \frac{\frac{1}{2 \sqrt{a + 2 x}} \times 2}{\frac{1}{2 \sqrt{x}}}$

$= {lim}_{x \to a} \frac{\sqrt{x}}{2 \sqrt{a + 2 x}}$

$= \frac{1}{2} \sqrt{\frac{a}{3 a}}$

$= \frac{1}{2 \sqrt{3}}$

Hence, this is the required answer.

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Similar questions

Q. If

I = \int \frac{(2 x - 3)^{1 / 2}}{(2 x - 3)^{1 / 3} + 1} d x

= 3 [\frac{1}{7} (2 x - 3)^{7 / 6} - \frac{1}{5} (2 x - 3)^{5 / 6} + \frac{1}{3} (2 x - 3)^{1 / 2} - (2 x - 3)^{1 / 6} + g (x)] + C

then g(x) is equal to

Q. Differentiate

{tan}^{- 1} (\frac{3 a^{2} x - x^{3}}{a^{3} - 3 a x^{2}})

- \frac{1}{\sqrt{3}} < \frac{x}{a} < \frac{1}{\sqrt{3}}

Q. Select the expression you will get for x and y if you solve the following equations using the cross multiplication method.

\sqrt{3} x = 2

\frac{x}{3} = 7 - \frac{y}{5}

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

Take away:

$(i) \frac{6}{5} x^{2} - \frac{4}{5} x^{3} + \frac{5}{6} + \frac{3}{2} x from \frac{x^{3}}{3} - \frac{5}{2} x^{2} + \frac{3}{5} x + \frac{1}{4}$

$(i i) \frac{5 a^{2}}{2} + \frac{3 a^{3}}{2} + \frac{a}{3} - \frac{6}{5} from \frac{1}{3} a^{3} - \frac{3}{4} a^{2} - \frac{5}{2}$

$(i i i) \frac{7}{4} x^{3} + \frac{3}{5} x^{2} + \frac{1}{2} x + \frac{9}{2} from \frac{7}{2} - \frac{x}{3} - \frac{x^{2}}{5}$

$(i v) \frac{y^{3}}{3} + \frac{7}{3} y^{2} + \frac{1}{2} y + \frac{1}{2} from \frac{1}{3} - \frac{5}{3} y^{2}$

$(v) \frac{2}{3} a c - \frac{5}{7} a b + \frac{2}{3} b c from \frac{3}{2} a b - \frac{7}{4} a c - \frac{5}{6} b c$

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limx→a√a+2x−√3a√x−√a

The correct option is D =12√3Consider the following differential eq. limx→a√a+2x−√3a√x−√a Using the L- Hospital rules, =limx→a12√a+2x×212√x =limx→a√x2√a+2x =12√a3a =12√3 Hence, this is the required answer.

$lim x \to a \frac{\sqrt{a + 2 x} - \sqrt{3 a}}{\sqrt{x} - \sqrt{a}}$