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Find the limit of $\frac{2y^2-3y+5}{y^2-5y+2}$ as $y$ approaches $\infty $

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Solving: $\lim_{y\to\infty }\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$
Solve instead: $\lim_{x\to\infty}\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

Solution

Formulas

Videos

Limit of (sin x)/x as x approaches 0

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Algebra 2 - Learn how to rationalize the denominator to simplify an expression, sqrt(y)/sqrt(5)

https://www.youtube.com/watch?v=G1Z66nMlBF0

Algebra 2 - Dividing two rational expressions (x^2/x^2 - y^2) / (4x/y-x)

https://www.youtube.com/watch?v=5MNXHwO_COA

Algebra 2 - How to find the zeros by factoring as well as label the multiplicity, y=x^4 -8x^3 -16x^2

https://www.youtube.com/watch?v=ZIlO0weAZ10

Worked example: Rewriting limit of Riemann sum as definite integral | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=Himr2l8Rd18

Function Plot

Plotting: $\frac{2y^2-3y+5}{y^2-5y+2}$

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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
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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Similar Problems Solved

Find the limit

$\lim_{x\to\infty}\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

Find the limit

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

Find the limit

$\lim_{y\to\infty}\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{e^{5x}-1-5x}{x^2}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{\sqrt{4+x}-2}{x}\right)$

Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

Used Formulas

See formulas (6)

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