Find the limit of $\left(\frac{\sqrt[6]{6x+16}-2}{\frac{1}{x}-\frac{1}{8}}\right)^{2x^3}$ as $x$ approaches $8$

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Final answer to the problem

indeterminate

Step-by-step Solution

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The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

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$L.C.M.=8x$

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Learn how to solve definite integrals problems step by step online. Find the limit of (((6x+16)^(1/6)-2)/(1/x-1/8))^(2x^3) as x approaches 8. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Combine and simplify all terms in the same fraction with common denominator 8x. Divide fractions \frac{\sqrt[6]{6x+16}-2}{\frac{8-x}{8x}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final answer to the problem

indeterminate

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Function Plot

Plotting: $\left(\frac{\sqrt[6]{6x+16}-2}{\frac{1}{x}-\frac{1}{8}}\right)^{2x^3}$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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