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

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Final answer to the problem

$-\frac{5}{2}$
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Step-by-step Solution

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Apply the formula: $\lim_{x\to c}\left(a\right)$$=\lim_{x\to c}\left(a\frac{conjugate\left(numerator\left(a\right)\right)}{conjugate\left(numerator\left(a\right)\right)}\right)$, where $a=\sqrt{x^2-5x+6}-x$ and $c=\infty $

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

Learn how to solve les limites de l'infini problems step by step online.

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

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Learn how to solve les limites de l'infini problems step by step online. (x)->(infinity)lim((x^2-5x+6)^(1/2)-x). Apply the formula: \lim_{x\to c}\left(a\right)=\lim_{x\to c}\left(a\frac{conjugate\left(numerator\left(a\right)\right)}{conjugate\left(numerator\left(a\right)\right)}\right), where a=\sqrt{x^2-5x+6}-x and c=\infty . Apply the formula: \lim_{x\to c}\left(a\right)=\lim_{x\to c}\left(a\right), where a=\left(\sqrt{x^2-5x+6}-x\right)\frac{\sqrt{x^2-5x+6}+x}{\sqrt{x^2-5x+6}+x} and c=\infty . Cancel like terms x^2 and -x^2. Apply the formula: \lim_{x\to c}\left(\frac{a}{b}\right)=\lim_{x\to c}\left(\frac{\frac{a}{sign\left(c\right)fgrow\left(b\right)}}{\frac{b}{sign\left(c\right)fgrow\left(b\right)}}\right), where a=-5x+6, b=\sqrt{x^2-5x+6}+x, c=\infty , a/b=\frac{-5x+6}{\sqrt{x^2-5x+6}+x} and x->c=x\to\infty .

Final answer to the problem

$-\frac{5}{2}$

Exact Numeric Answer

$-2.5$

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Function Plot

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

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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

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