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Find the limit of $x\left(\sqrt{3}x-\sqrt{3x^2+1}\right)$ as $x$ approaches $\infty $

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Solution

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Final answer to the problem

$c-f$
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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(3^(1/2)x-(3x^2+1)^(1/2)) as x approaches infinity. Multiply the single term x by each term of the polynomial \left(\sqrt{3}x-\sqrt{3x^2+1}\right). When multiplying two powers that have the same base (x), you can add the exponents. Applying rationalisation. Multiply and simplify the expression within the limit.

Final answer to the problem

$c-f$

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Function Plot

Plotting: $x\left(\sqrt{3}x-\sqrt{3x^2+1}\right)$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻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.

Used Formulas

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