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Find the limit of $\sqrt{x^2+x+1}-2x$ as $x$ approaches $\infty $

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Solution

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Final answer to the problem

$- \infty $
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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+1)^(1/2)-2x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. The power of a product is equal to the product of it's factors raised to the same power. Multiply -1 times 4.

Final answer to the problem

$- \infty $

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Function Plot

Plotting: $\sqrt{x^2+x+1}-2x$

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7
8
9
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

How to improve your answer:

Similar Problems Solved

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Find the limit

$\lim_{x\to\infty}\left(\frac{1}{x^2}\right)$

Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

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