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Q. 17

Expert-verifiedFound in: Page 883

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

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.

We know,

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

The simplified expression is

$\underset{x\to -1}{\mathrm{lim}}\left(3{x}^{2}-5x\right)=\underset{x\to -1}{\mathrm{lim}}3{x}^{2}-\underset{x\to -1}{\mathrm{lim}}5x\phantom{\rule{0ex}{0ex}}=\{3\times {\left(1\right)}^{2}\}-\{5\times -1\}\phantom{\rule{0ex}{0ex}}=3-(-5)\phantom{\rule{0ex}{0ex}}=3+5\phantom{\rule{0ex}{0ex}}=8$

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