Final answer to the problem
$\sqrt{c-f}$
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Step-by-step Solution
How should I solve this problem?
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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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1
Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$
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$\sqrt{\lim_{x\to\infty }\left(4x+\sqrt{4x+\sqrt{4x-2\sqrt{x}}}\right)}$
Learn how to solve problems step by step online. Find the limit of (4x+(4x+(4x-2x^(1/2))^(1/2))^(1/2))^(1/2) as x approaches infinity. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. Applying rationalisation. Multiply and simplify the expression within the limit. The power of a product is equal to the product of it's factors raised to the same power.
Final answer to the problem
$\sqrt{c-f}$
