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Step-by-step Solution

Evaluate the limit of $\frac{x^2-4}{x-2}$ as $x$ approaches $2$

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Step-by-step explanation

Problem to solve:

$\lim_{x\to2}\left(\frac{x^2-4}{x-2}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to2}\left(x+2\right)$

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of (x^2-4)/(x-2) as x approaches 2. Factor the difference of squares x^2-4 as the product of two conjugated binomials. 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)). The limit of a constant is just the constant. Evaluate the limit by replacing all occurrences of x by 2.

Answer

$4$

Problem Analysis

$\lim_{x\to2}\left(\frac{x^2-4}{x-2}\right)$

Main topic:

Limits

Related formulas:

2. See formulas

Time to solve it:

~ 0.05 seconds