Solve this limit when x tends to +infinity

  • Thread starter mohlam12
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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
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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
 
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  • #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 :rofl:
 
Last edited:
  • #5
yes.. but it is an indeterminate form... how is it equal to zero
 

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

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