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Quotient of powers Calculator

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1

Solved example of Quotient of powers

$\lim_{x\to1}\left(x-1\right)\cdot \tan\left(\frac{\pix}{2}\right)$
2

Take $\frac{\pi }{2}$ out of the fraction

$\lim_{x\to1}\left(x-1\right)\tan\left(\sqrt{2}x\right)$
3

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\left(\lim_{x\to1}\left(x\right)+\lim_{x\to1}\left(-1\right)\right)\tan\left(\sqrt{2}x\right)$
4

Multiplying polynomials $\tan\left(\sqrt{2}x\right)$ and $\lim_{x\to1}\left(x\right)+\lim_{x\to1}\left(-1\right)$

$\lim_{x\to1}\left(x\right)\tan\left(\sqrt{2}x\right)+\lim_{x\to1}\left(-1\right)\tan\left(\sqrt{2}x\right)$
5

The limit of a constant is just the constant

$\lim_{x\to1}\left(x\right)\tan\left(\sqrt{2}x\right)-\tan\left(\sqrt{2}x\right)$
6

Evaluating the limit when $x$ tends to $1$

$1\tan\left(\sqrt{2}x\right)-\tan\left(\sqrt{2}x\right)$
7

Simplifying

$\tan\left(\sqrt{2}x\right)-\tan\left(\sqrt{2}x\right)$
8

Subtracting $\tan\left(\sqrt{2}x\right)$ and $\tan\left(\sqrt{2}x\right)$

$0$

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