Final answer to the problem
$x$
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Step-by-step Solution
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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
Applying rationalisation
$x\lim_{t\to3}\left(\frac{3-t}{\sqrt{t+1}-\sqrt{5t-11}}\frac{\sqrt{t+1}+\sqrt{5t-11}}{\sqrt{t+1}+\sqrt{5t-11}}\right)$
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$x\lim_{t\to3}\left(\frac{3-t}{\sqrt{t+1}-\sqrt{5t-11}}\frac{\sqrt{t+1}+\sqrt{5t-11}}{\sqrt{t+1}+\sqrt{5t-11}}\right)$
Learn how to solve problems step by step online. Find the limit x((t)->(3)lim((3-t)/((t+1)^(1/2)-(5t-11)^(1/2)))). Applying rationalisation. Multiplying fractions \frac{3-t}{\sqrt{t+1}-\sqrt{5t-11}} \times \frac{\sqrt{t+1}+\sqrt{5t-11}}{\sqrt{t+1}+\sqrt{5t-11}}. Solve the product of difference of squares \left(\sqrt{t+1}-\sqrt{5t-11}\right)\left(\sqrt{t+1}+\sqrt{5t-11}\right). Combining like terms t and -5t.
Final answer to the problem
$x$
