Final answer to the problem
$-\frac{1}{48}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
$\lim_{x\to6}\left(\frac{6-x}{\left(x^2-36\right)\left(2+\sqrt{x-2}\right)}\frac{6+x}{6+x}\right)$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to6}\left(\frac{6-x}{\left(x^2-36\right)\left(2+\sqrt{x-2}\right)}\frac{6+x}{6+x}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of (6-x)/((x^2-36)(2+(x-2)^(1/2))) as x approaches 6. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \frac{36-x^2}{\left(x^2-36\right)\left(2+\sqrt{x-2}\right)\left(6+x\right)} multiplying the denominator by -1. Evaluate the limit \lim_{x\to6}\left(\frac{-1}{\left(2+\sqrt{x-2}\right)\left(6+x\right)}\right) by replacing all occurrences of x by 6.
Final answer to the problem
$-\frac{1}{48}$
Exact Numeric Answer
$-0.0208333$
