For all values of $x$ , find the expression equivalent to $x^{\frac{5}{7}}$ .

\frac{5}{x^{7}}

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\frac{1}{x^{2}}

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\sqrt[5]{x^{7}}

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\sqrt[7]{x^{5}}

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Solution

The correct option is D $\sqrt[7]{x^{5}}$
The given expression can be written as $(x^{5})^{\frac{1}{7}}$
Example: we can write $x^{\frac{1}{2}} = \sqrt{x}$
Likewise, we write the expression as $\sqrt[7]{x^{5}}$

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$t a n x = x + \frac{x^{3}}{3} + \frac{2. x^{5}}{15} . . . . . .$

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$s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$

$t a n x = x + \frac{x^{3}}{3} + \frac{2. x^{5}}{15} . . . . . .$

Find the value of $lim x \to 0 \frac{x c o s x + s i n x}{x^{2} + t a n x}$

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