QuestionAugust 25, 2025

(1 point) Evaluate the limit lim _(xarrow -10)((1+5x)/(1-8x))^3 Enter DNE if the limit does not exist. Limit=square

(1 point) Evaluate the limit lim _(xarrow -10)((1+5x)/(1-8x))^3 Enter DNE if the limit does not exist. Limit=square
(1 point) Evaluate the limit
lim _(xarrow -10)((1+5x)/(1-8x))^3
Enter DNE if the limit does not exist.
Limit=square

Solution
4.0(277 votes)

Answer

\frac{-117649}{531441} Explanation 1. Substitute the limit value Substitute x = -10 into the expression \left(\frac{1+5x}{1-8x}\right)^3. 2. Calculate the numerator Calculate 1 + 5(-10) = 1 - 50 = -49. 3. Calculate the denominator Calculate 1 - 8(-10) = 1 + 80 = 81. 4. Simplify the fraction The fraction becomes \frac{-49}{81}. 5. Evaluate the cube Calculate \left(\frac{-49}{81}\right)^3 = \frac{(-49)^3}{81^3}.

Explanation

1. Substitute the limit value<br /> Substitute $x = -10$ into the expression $\left(\frac{1+5x}{1-8x}\right)^3$.<br />2. Calculate the numerator<br /> Calculate $1 + 5(-10) = 1 - 50 = -49$.<br />3. Calculate the denominator<br /> Calculate $1 - 8(-10) = 1 + 80 = 81$.<br />4. Simplify the fraction<br /> The fraction becomes $\frac{-49}{81}$.<br />5. Evaluate the cube<br /> Calculate $\left(\frac{-49}{81}\right)^3 = \frac{(-49)^3}{81^3}$.
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