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# Find the limit of $\frac{2-\sqrt{x-3}}{x^2-49}$ as $x$ approaches $7$

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$-\frac{1}{56}$$\,\,\left(\approx -0.017857142857142856\right) Got another answer? Verify it here ## Step-by-step Solution Problem to solve: \lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\right) Choose the solving method 1 Applying rationalisation \lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}\right) Learn how to solve limits by factoring problems step by step online. \lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}\right) Learn how to solve limits by factoring problems step by step online. Find the limit of (2-(x-3)^0.5)/(x^2-49) as x approaches 7. Applying rationalisation. Multiplying fractions \frac{2-\sqrt{x-3}}{x^2-49} \times \frac{2+\sqrt{x-3}}{2+\sqrt{x-3}}. Solve the product of difference of squares \left(2-\sqrt{x-3}\right)\left(2+\sqrt{x-3}\right). Expand and simplify 4-\left(x-3\right). ## Final Answer -\frac{1}{56}$$\,\,\left(\approx -0.017857142857142856\right)$
SnapXam A2

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π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\lim_{x\to7}\left(\frac{2-\sqrt{x-3}}{x^2-49}\right)$