Solve this limit when x tends to +infinity

  • Thread starter mohlam12
  • Start date
  • Tags
    Limit
In summary, the conversation is about solving a limit as x tends to +infinity without using the L'Hopital rule. The limit in question involves the expression (\frac{3}{2})^{x}\frac{(\frac{x^{\frac{2}{3}}}{3^{x}})-1}{(\frac{x^{\frac{5}{2}}}{2^{x}})+1}. The person tried to factorize the expression but was unable to come to a result. They also mentioned that the limit of (\frac{3}{2})^{x} is +infinity and they need to show that the limit of \frac{x^{2/3}}{3^x} is zero. They are unsure how
  • #1
mohlam12
154
0
please
any hints to solve this limit when x tends to +infinity is way very appreciated !
PS: i should not use the hopital rule...
I tried to factorize the x from the nominator and denominator but couldn't get to any result... i tried some other things.. but still nothing.

[tex]\frac{x^{\frac{2}{3}} - 3^{x}}{x^{\frac{5}{2}} + 2^{x}}[/tex]

thanks very much
 
Physics news on Phys.org
  • #2
Rewrite this as:
[tex](\frac{3}{2})^{x}\frac{(\frac{x^{\frac{2}{3}}}{3^{x}})-1}{(\frac{x^{\frac{5}{2}}}{2^{x}})+1}[/tex]
 
  • #3
okay the limit of (3/2)^x is +infinity
but i have to show that the limit of [tex]\frac{x^{2/3}}{3^x}[/tex] is zero... how ?? maybe I have to show that it is smaller than a number, then the limit of that number should be zero... by the way, we haven't studied exponentials yet..

PS: I think this should be moved to calculus and beyond ?
 
Last edited:
  • #4
the limit of [tex]\frac{x^{2/3}}{3^x}[/tex] goes to zero.

EDIT: Latex is so texy :smile:
 
Last edited:
  • #5
yes.. but it is an indeterminate form... how is it equal to zero
 

FAQ: Solve this limit when x tends to +infinity

What does it mean to solve a limit when x tends to infinity?

When we say "solve a limit when x tends to infinity," we are referring to finding the value that a function approaches as the input (x) gets larger and larger, approaching infinity.

How do I know if a limit when x tends to infinity exists?

A limit when x tends to infinity exists if the function has a finite value as x approaches infinity. This means that the function is approaching a specific value and not growing or decreasing without bound.

Can a limit when x tends to infinity be negative?

Yes, a limit when x tends to infinity can be negative. It all depends on the behavior of the function as x gets larger and larger. The limit can approach a negative value, or it can approach zero from the negative side.

What are some common techniques for solving limits when x tends to infinity?

Some common techniques for solving limits when x tends to infinity include evaluating the limit algebraically, using L'Hôpital's rule, or using the properties of limits such as the Squeeze Theorem.

Why is it important to solve limits when x tends to infinity?

Solving limits when x tends to infinity allows us to understand the behavior of a function as the input gets larger and larger. This can help us make predictions about the function and its overall trend, which can be useful in various fields of science and mathematics.

Similar threads

Finding the direction of infinite limits
Replies
10
Views
1K
Proving the result of the following limit
Replies
10
Views
1K
Limit question to be done without using derivatives
Replies
25
Views
1K
Calculating Left Hand Limit: ##\sqrt 6##
Replies
17
Views
1K
Calculating the Limit of (1 + 2^x)^(2^(-x))
Replies
5
Views
1K
To find the boundedness of a given function
Replies
14
Views
2K
Evaluating a limit as x tends to ## \infty##
Replies
20
Views
3K
Finding the limit of a quotient as x goes to minus infinity
Replies
6
Views
2K
Finding the domain (and range) of a logarithmic function
Replies
11
Views
2K
Need help in manipulating rational absolute value inequalities
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top