Solve limit (as x approaches -3) of x^2-9/x^2+2x-3 | Microsoft Math Solver

Evaluate

\frac{3}{2} = 1.5

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5 problems similar to:

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}

Similar Problems from Web Search

What is the value of

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} - 2 x - 1 5}

https://socratic.org/questions/what-is-the-value-of-lim-x-rightarrow-3-frac-x-2-9-x-2-2x-15

\frac{3}{4}

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} - 2 x - 1 5}

By factoring out the numerator and the denominator,

= x \to - 3 lim \frac{( x + 3 ) ( x - 3 )}{( x + 3 ) ( x - 5 )} = \frac{- 3 - 3}{- 3 - 5} = \frac{- 6}{- 8} = \frac{3}{4}

x \to - 3 lim \frac{x ^{2} - 9}{2 x ^{2} + 7 x + 3}

https://math.stackexchange.com/q/490053

Note that both the numerator and denominator evaluate to

0

x = - 3

. That means we have an indeterminate limit, which simply means more work needs to be done. Factor ...

Help with epsilon-delta proof of

lim_{x \to - 3} \frac{x ^{2} + x - 6}{x ^{2} - 9}

https://math.stackexchange.com/questions/197844/help-with-epsilon-delta-proof-of-lim-x-to-3-fracx2-x-6x2-9

\frac{x ^{2} + x - 6}{x ^{2} - 9} - \frac{5}{6} = \frac{6 x ^{2} + 6 x - 3 6 - ( 5 x ^{2} - 4 5 )}{6 ( x ^{2} - 9 )} = \frac{x ^{2} + 6 x + 9}{6 ( x ^{2} - 9 )} = \frac{( x + 3 ) ^{2}}{6 ( x - 3 ) ( x + 3 )}

x \to 1 lim \frac{x ^{2} - 1}{x ^{2} + 3 x - 4}

https://www.quora.com/What-is-displaystyle-lim_-x-to-1-dfrac-x-2-1-x-2+3x-4

You can see if you solve for

x = 1

that you get a fraction in the form of

\frac{0}{0}

which is indeterminate. When you get into a situation like this you can apply L'Hôpital's rule - Wikipedia. ...

lim_{x \to 2} \frac{x ^{2} - 5 x}{x ^{2} + 2} = - 1

ϵ

δ

definition of a limit

https://math.stackexchange.com/questions/1872290/proving-that-lim-x-to-2-fracx2-5xx22-1-using-the-epsilon-delta

ϵ > 0

be given. We have to find a number

δ > 0

∣ ∣ ∣ ∣ \frac{x ^{2} - 5 x}{x ^{2} + 2} + 1 ∣ ∣ ∣ ∣ < ϵ

∣ x - 2 ∣ < δ

. But, as Andre notes,

∣ ∣ ∣ ∣ \frac{x ^{2} - 5 x}{x ^{2} + 2} + 1 ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \frac{2 x ^{2} - 5 x + 2}{x ^{2} + 2} ∣ ∣ ∣ ∣ = ∣ x - 2 ∣ ∣ ∣ ∣ \frac{2 x - 1}{x ^{2} + 1} ∣ ∣ ∣ .

Limit simplification

https://math.stackexchange.com/q/2704118

lim_{x \to - 3} \frac{( x ^{2} - 9 ) ^{2}}{x ^{2} + 6 x + 9}

We can solve in this way

lim_{x \to - 3} \frac{( x ^{2} - 9 ) ^{2}}{( x + 3 ) ^{2}} = lim_{x \to - 3} \frac{( x - 3 ) ^{2} ( x + 3 ) ^{2}}{( x + 3 ) ^{2}} = lim_{x \to - 3} (x - 3)^{2} = 36

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x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}