👉 Try now NerdPal! Our new math app on iOS and Android

Find the limit of $\frac{\left(2x-1\right)^{\left(x-2\right)}}{\left(2x+3\right)^{\left(x-2\right)}}$ as $x$ approaches $\infty $

Step-by-step Solution

Go!
Math mode
Text mode
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

Final Answer

indeterminate

Step-by-step Solution

Specify the solving method

1

Evaluate the limit $\lim_{x\to\infty }\left(\frac{\left(2x-1\right)^{\left(x-2\right)}}{\left(2x+3\right)^{\left(x-2\right)}}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{\left(2\cdot \infty -1\right)^{\left(\infty -2\right)}}{\left(2\cdot \infty +3\right)^{\left(\infty -2\right)}}$

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

$\frac{\left(2\cdot \infty -1\right)^{\left(\infty -2\right)}}{\left(2\cdot \infty +3\right)^{\left(\infty -2\right)}}$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve limits to infinity problems step by step online. Find the limit of ((2x-1)^(x-2))/((2x+3)^(x-2)) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\frac{\left(2x-1\right)^{\left(x-2\right)}}{\left(2x+3\right)^{\left(x-2\right)}}\right) by replacing all occurrences of x by \infty . Any expression multiplied by infinity tends to infinity, in other words: \infty\cdot(\pm n)=\pm\infty, if n\neq0. Any expression multiplied by infinity tends to infinity, in other words: \infty\cdot(\pm n)=\pm\infty, if n\neq0. Infinity plus any algebraic expression is equal to infinity.

Final Answer

indeterminate

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

Give us your feedback!

Function Plot

Plotting: $\frac{\left(2x-1\right)^{\left(x-2\right)}}{\left(2x+3\right)^{\left(x-2\right)}}$

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.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account