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Solving: $\lim_{x\to{2x+1}}\left(x^2-2x+5\right)$
Solve instead: $\lim_{x\to2y+1}\left(x^2-2x+5\right)$

Exercise

$\lim_{x\to2y+1}\left(x^2-2x+5\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to{2x+1}}\left(x^2-2x+5\right)$ by replacing all occurrences of $x$ by $2x+1$

$\left(2x+1\right)^2-2\left(2x+1\right)+5$
2

Multiply the single term $-2$ by each term of the polynomial $\left(2x+1\right)$

$\left(2x+1\right)^2-4x-2+5$
3

Add the values $-2$ and $5$

$\left(2x+1\right)^2-4x+3$

Final answer to the exercise

$\left(2x+1\right)^2-4x+3$

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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