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Find the limit of $\frac{5x^2-7x}{9x^2+9}$ as $x$ approaches $\infty $

Step-by-step Solution

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Solution

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Final Answer

$\frac{5}{9}$
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Step-by-step Solution

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Multiply the single term $9$ by each term of the polynomial $\left(x^2+1\right)$

$\lim_{x\to\infty }\left(\frac{5x^2-7x}{9x^2+9}\right)$

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

$\lim_{x\to\infty }\left(\frac{5x^2-7x}{9x^2+9}\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit of (5x^2-7x)/(9x^2+9) as x approaches infinity. Multiply the single term 9 by each term of the polynomial \left(x^2+1\right). As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction .

Final Answer

$\frac{5}{9}$

Exact Numeric Answer

$0.5556$

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Function Plot

Plotting: $\frac{5x^2-7x}{9x^2+9}$

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◻/◻
/
÷
◻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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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.

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