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Evaluate the limit lim x->2 (x^2 - 4)/(x - 2).
Evaluate the limit lim x->2 (x^2 - 4)/(x - 2).
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Q1
Evaluate the limit lim x->2 (x^2 - 4)/(x - 2).
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4
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Factoring gives (x-2)(x+2)/(x-2). Canceling gives lim x->2 (x + 2) = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the limit lim x->2 (x^2 - 4)/(x - 2).
Solution:
Factoring gives (x-2)(x+2)/(x-2). Canceling gives lim x->2 (x + 2) = 4.
Steps: 9
Show Steps
Step 1: Identify the limit you need to evaluate: lim x->2 (x^2 - 4)/(x - 2).
Step 2: Notice that the expression (x^2 - 4) can be factored. It is a difference of squares.
Step 3: Factor (x^2 - 4) into (x - 2)(x + 2).
Step 4: Rewrite the limit with the factored expression: lim x->2 ((x - 2)(x + 2))/(x - 2).
Step 5: You can see that (x - 2) is in both the numerator and the denominator.
Step 6: Cancel (x - 2) from the numerator and the denominator, which simplifies the expression to lim x->2 (x + 2).
Step 7: Now, substitute x = 2 into the simplified expression (x + 2).
Step 8: Calculate (2 + 2) which equals 4.
Step 9: Therefore, the limit is 4.
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