"Evaluate the following limits. a) limx→32+18x3−2x b) limx→32−18x3−2x" was answered by our experts

Bergen

Answered question

2021-10-27

Evaluate the following limits.
a)

lim_{x \to {\frac{3}{2}}^{+}} \frac{18 x}{3 - 2 x}

lim_{x \to {\frac{3}{2}}^{-}} \frac{18 x}{3 - 2 x}

diskusje5

Skilled2021-10-28Added 82 answers

lim_{x \to {\frac{3}{2}}^{+}} \frac{18 x}{3 - 2 x}

lim_{x \to \frac{3^{+}}{2}} \frac{18 x}{3 - 2 x}

As,

x \to {\frac{3}{2}}^{+}, (3 - 2 x) \to 0^{-}

And,

\frac{a}{0^{-}} \to - \infty

\Rightarrow lim_{x \to \frac{3^{+}}{2}} \frac{18 x}{3 - 2 x} = - \infty

lim_{x \to {\frac{3}{2}}^{-}} \frac{18 x}{3 - 2 x}

lim_{x \to \frac{3^{-}}{2}} \frac{18 x}{3 - 2 x}

As,

x \to {\frac{3}{2}}^{-}, (3 - 2 x) \to 0^{+}

And,

\frac{a}{0^{+}} \to \infty

\Rightarrow lim_{x \to \frac{3^{-}}{2}} \frac{18 x}{3 - 2 x} = \infty

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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