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Step-by-step Solution

Find the limit of $x^2-5x-6$ as $x$ approaches $0$

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Answer

$-6$

Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(x^2-5x-6\right)$
1

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\lim_{x\to0}\left(x^2\right)+\lim_{x\to0}\left(-5x\right)+\lim_{x\to0}\left(-6\right)$
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The limit of a constant is just the constant

$\lim_{x\to0}\left(x^2\right)+\lim_{x\to0}\left(-5x\right)-6$

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Answer

$-6$
$\lim_{x\to0}\left(x^2-5x-6\right)$

Main topic:

Limits

Used formulas:

2. See formulas

Time to solve it:

~ 0.42 seconds

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