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Find the limit of $\frac{x^2-x-6}{\sqrt{3x+4}-\sqrt{5x-2}}$ as $x$ approaches $3$

Step-by-step Solution

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Solution

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Final answer to the problem

$-5\sqrt{13}$
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Step-by-step Solution

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of (x^2-x+-6)/((3x+4)^(1/2)-(5x-2)^(1/2)) as x approaches 3. Applying rationalisation. Multiplying fractions \frac{x^2-x-6}{\sqrt{3x+4}-\sqrt{5x-2}} \times \frac{\sqrt{3x+4}+\sqrt{5x-2}}{\sqrt{3x+4}+\sqrt{5x-2}}. Solve the product of difference of squares \left(\sqrt{3x+4}-\sqrt{5x-2}\right)\left(\sqrt{3x+4}+\sqrt{5x-2}\right). Combining like terms 3x and -5x.

Final answer to the problem

$-5\sqrt{13}$

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Function Plot

Plotting: $\frac{x^2-x-6}{\sqrt{3x+4}-\sqrt{5x-2}}$

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◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

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