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Exercise

$\lim_{x\to3}\left(x^2+2x-7\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to3}\left(x^2+2x-7\right)$ by replacing all occurrences of $x$ by $3$

$3^2+2\cdot 3-7$
2

Multiply $2$ times $3$

$3^2+6-7$
3

Subtract the values $6$ and $-7$

$3^2-1$
4

Calculate the power $3^2$

$9-1$
5

Subtract the values $9$ and $-1$

$8$

Final answer to the exercise

$8$

Try other ways to solve this exercise

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • 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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$\lim_{x\to-4}\left(\frac{x+4}{x^2-16}\right)$

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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