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Exercise

$\sqrt{2x\cdot\sqrt{8x^3}}$

Roots of the equation

$x^{\left(\frac{1}{2}+3\cdot \left(\frac{1}{2}\right)^2\right)}=\frac{0}{\left(\sqrt{8}\right)^2}$
See step-by-step solution

Limit of this function

$\lim_{x\to0}\left(\sqrt{2x\sqrt{8x^3}}\right)=\lim_{x\to0}\left(\sqrt{2}\cdot \left(\sqrt{8}\right)^2x^{\left(\frac{1}{2}+3\cdot \left(\frac{1}{2}\right)^2\right)}\right)$
See step-by-step solution

Derivative of this function

$\frac{d}{dx}\left(\sqrt{2x\sqrt{8x^3}}\right)=\sqrt{2}\cdot \left(\sqrt{8}\right)^2\cdot \left(\frac{1}{2}+3\cdot \left(\frac{1}{2}\right)^2\right)x^{\left(-\frac{1}{2}+3\cdot \left(\frac{1}{2}\right)^2\right)}$
See step-by-step solution

Integral of this function

$\int\sqrt{2x\sqrt{8x^3}}dx=\frac{4\sqrt{2}\sqrt[4]{8}\sqrt[4]{x^{9}}}{9}+C_0$
See step-by-step solution

Try other ways to solve this exercise

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  • Solve by quadratic formula (general formula)
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  • Find the roots
  • Find break even points
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