Limits Calculator

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Example

Created on 2024-06-20Asked by Victoria Harris (Solvelet student)

Find the limit:

\lim_{x \to 2} \frac{x^2 - 4}{x - 2}

Solution

To find the limit

\lim_{x \to 2} \frac{x^2 - 4}{x - 2}

, we notice that direct substitution results in an indeterminate form

\frac{0}{0}

. Therefore, we factorize the numerator:

x^2 - 4 = (x - 2)(x + 2)

Thus, the limit becomes:

\lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}

We can cancel the common factor

(x - 2)

in the numerator and denominator:

\lim_{x \to 2} (x + 2)

Now, we substitute

x = 2

\lim_{x \to 2} (x + 2) = 2 + 2 = 4

Therefore, the limit is:

4

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Samuel Lewis on Solvelet

1. Evaluate

\lim_{x \to 1} \frac{x^2 - 1}{x - 1}

,2. Find the value of

c

that makes the function

f(x) = \begin{cases} x^2 + c, & x < 2 \\ 3x - 1, & x \geq 2 \end{cases}

continuous at

x = 2

DefinitionWhat does a Limits Calculator do Definition: A Limits Calc evaluates the limet of a function when the input approaches a certain value. For example, a calculator would simply simplify and evaluate the expression ( \lim_{{x \to 2}} (x^2-4)/(x-2) ) by calculating: \[\lim_{{x\to2}}\frac{{\left( x-2 \right)\left( x+2 \right)}}{{x-2}}=\lim_{{x\to2}}\left( x+2 \right)=4\].

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