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Exercise

$\lim_{a\to0}\left(\left(\frac{1}{2}a^2+1\right)^2\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{a\to0}\left(\left(\frac{1}{2}a^2+1\right)^2\right)$ by replacing all occurrences of $a$ by $0$

$\left(\frac{1}{2}\cdot 0^2+1\right)^2$
2

Calculate the power $0^2$

$\left(0\left(\frac{1}{2}\right)+1\right)^2$
3

Any expression multiplied by $0$ is equal to $0$

$1^2$
4

Calculate the power $1^2$

$1$

Final answer to the exercise

$1$

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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