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Answers without the blur. Sign up and see all textbooks for free! Q. 17

Expert-verified Found in: Page 883 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # In Problems 7– 42, find each limit algebraically $\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)$

The value of the limit$\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)=8$

See the step by step solution

## Step 1. Given Information

The given limit function is$\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)$

We need to find the value of the limit.

## Step 2. Expanding the limit

We know,

$\underset{x\to c}{\mathrm{lim}}\left[f\left(x\right)-g\left(x\right)\right]=\underset{x\to c}{\mathrm{lim}}f\left(x\right)-\underset{x\to c}{\mathrm{lim}}g\left(x\right)\phantom{\rule{0ex}{0ex}}Therefore,\phantom{\rule{0ex}{0ex}}\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)=\underset{x\to -1}{\mathrm{lim}}3{x}^{2}-\underset{x\to -1}{\mathrm{lim}}5x\phantom{\rule{0ex}{0ex}}$

## Step 3. Value of the limit

The simplified expression is

$\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)=\underset{x\to -1}{\mathrm{lim}}3{x}^{2}-\underset{x\to -1}{\mathrm{lim}}5x\phantom{\rule{0ex}{0ex}}=\left\{3×{\left(1\right)}^{2}\right\}-\left\{5×-1\right\}\phantom{\rule{0ex}{0ex}}=3-\left(-5\right)\phantom{\rule{0ex}{0ex}}=3+5\phantom{\rule{0ex}{0ex}}=8$ ### Want to see more solutions like these? 