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Exercise

$\lim_{x\to1}\left(\left\{x+1\right\}\left\{x-1\right\}\right)$

Step-by-step Solution

1

The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.

$\lim_{x\to1}\left(x^2-1\right)$
2

Evaluate the limit $\lim_{x\to1}\left(x^2-1\right)$ by replacing all occurrences of $x$ by $1$

$1^2-1$
3

Calculate the power $1^2$

$1-1$
4

Subtract the values $1$ and $-1$

0

Final answer to the exercise

0

Try other ways to solve this exercise

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  • Solve using limit properties
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  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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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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