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# Find the limit of $\sqrt{x^2-5x+6}-x$ as $x$ approaches $\infty$

## Step-by-step Solution

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$\infty$
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## Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty\:}\left(\sqrt{X^2-5X+6}-X\right)$

Specify the solving method

1

The limit of a polynomial function ($\sqrt{x^2-5x+6}-x$) when $x$ tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term

$\lim_{x\to\infty }\left(-x\right)$

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(-x\right)$

Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2-5x+6)^1/2-x as x approaches \infty. The limit of a polynomial function (\sqrt{x^2-5x+6}-x) when x tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Evaluate the limit \lim_{x\to\infty }\left(x\right) by replacing all occurrences of x by \infty .

$\infty$
SnapXam A2

### beta Got another answer? Verify it!

Go!
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0
a
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
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

$\lim_{x\to\infty\:}\left(\sqrt{X^2-5X+6}-X\right)$

### Main topic:

Limits to Infinity

~ 0.08 s