Limits by factoring Calculator

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Example

Created on 2024-06-20Asked by Evelyn Jones (Solvelet student)

Evaluate the limit

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

by factoring.

Solution

To evaluate the limit

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

by factoring, we factorize the numerator:

x^2 - 9 = (x - 3)(x + 3)

Thus, the limit becomes:

\lim_{x \to 3} \frac{(x - 3)(x + 3)}{x - 3}

We can cancel the common factor

(x - 3)

in the numerator and denominator:

\lim_{x \to 3} (x + 3)

Now, we substitute

x = 3

\lim_{x \to 3} (x + 3) = 3 + 3 = 6

Therefore, the limit is:

6

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jacob Mitchell on Solvelet

1. Compute

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

by factoring,2. Evaluate the limit

\lim_{x \to \infty} \frac{x^2}{e^x}

using L'Hopital's rule.

DefinitionA limits by factoring calculator is a calculator used for computing the limit of a rational function by factoring the polynomials in a way that removes common terms from the fraction. For Example: To solve ( \lim_{{x \to 3}} \frac{x^2 - 9}{x - 3} ) The left-hand side simplifies to \left[ \frac{(x-3)(x+3)}{x-3} = x + 3 \right] Limit_{x -> 3} (frac(x^2-9)(x-3) = They we substitute only the value of x = 3 As ( x > 3 ), ( x + 3 = 6 ) So ( lim_{x -> 3}frac(x^2-9)(x-3) = 6 )

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