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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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Final Answer

$\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.

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

Unlock the first 2 steps of this solution!

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 .

Final Answer

$\infty $
SnapXam A2
Answer Assistant

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Got another answer? Verify it!

Go!
1
2
3
4
5
6
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
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

Useful tips on how to improve your answer:

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

Main topic:

Limits to Infinity

Used formulas:

1. See formulas

Time to solve it:

~ 0.08 s