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Find the limit $\lim_{x\to5}\left(\frac{x^2-10x+25}{x^2-25}\right)$

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Step-by-step Solution

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The trinomial $x^2-10x+25$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=-10^2-4\left(1\right)\left(25\right) = 0$

Learn how to solve limits by direct substitution problems step by step online.

$\Delta=b^2-4ac=-10^2-4\left(1\right)\left(25\right) = 0$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(5)lim((x^2-10x+25)/(x^2-25)). The trinomial x^2-10x+25 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. Factor the difference of squares x^2-25 as the product of two conjugated binomials.

Final Answer

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Function Plot

Plotting: $\frac{x^2-10x+25}{x^2-25}$

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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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