Final Answer
$-\frac{1}{56}$$\,\,\left(\approx -0.017857142857142856\right)$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\right)$
Choose the solving method
1
Applying rationalisation
$\lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}\right)$
Learn how to solve limits by factoring problems step by step online.
$\lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}\right)$
Learn how to solve limits by factoring problems step by step online. Find the limit of (2-(x-3)^0.5)/(x^2-49) as x approaches 7. Applying rationalisation. Multiplying fractions \frac{2-\sqrt{x-3}}{x^2-49} \times \frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}. Solve the product of difference of squares \left(2-\sqrt{x-3}\right)\left(2+\sqrt{x-3}\right). Expand and simplify 4-\left(x-3\right).
Final Answer
$-\frac{1}{56}$$\,\,\left(\approx -0.017857142857142856\right)$