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Exercise

$\lim_{x\to4}\sqrt{4x}$

Step-by-step Solution

1

The power of a product is equal to the product of it's factors raised to the same power

$\lim_{x\to4}\left(\sqrt{4}\sqrt{x}\right)$
2

Calculate the power $\sqrt{4}$

$\lim_{x\to4}\left(2\sqrt{x}\right)$
3

Evaluate the limit $\lim_{x\to4}\left(2\sqrt{x}\right)$ by replacing all occurrences of $x$ by $4$

$2\sqrt{4}$
4

Calculate the power $\sqrt{4}$

$2\cdot 2$
5

Multiply $2$ times $2$

$4$

Final answer to the exercise

$4$

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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