Another limit homework problem

In summary, the question is whether lim_{x\rightarrow \infty} f(x)=0 implies lim_{x\rightarrow \infty} f'(x)=0, and if so, a proof is requested. Otherwise, a counter example is needed. \frac{sin(x^2)}{x} is given as a counter example.
  • #1
calculus_jy
56
0
This questions has been bothering me for quiet a while

Does [tex]lim_{x\rightarrow \infty} f(x)=0 \Rightarrow lim_{x\rightarrow \infty} f'(x)=0 [/tex] if so can you please post a proof because its giving me a headache. If not would it please be possible for you to give me a counter example.

Many thanks
 
Last edited:
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  • #2


calculus_jy said:
This questions has been bothering me for quiet a while

Does [tex]lim_{x\rightarrow \infty} f(x)=0 \Rightarrow lim_{x\rightarrow \infty} f'(x)=0 [/tex] if so can you please post a proof because its giving me a headache. If not would it please be possible for you to give me a counter example.

Many thanks

[tex]\frac{sin(x^2)}{x}[/tex]
 

1. What is a limit in mathematics?

A limit in mathematics refers to the value that a function or sequence approaches as the input or index approaches a certain value. It is used to describe the behavior of a function or sequence near a particular point.

2. How do I solve a limit homework problem?

To solve a limit homework problem, you need to first identify the type of limit (e.g. one-sided, infinite, etc.) and then apply the appropriate rules and techniques (e.g. algebraic manipulation, L'Hôpital's rule, etc.) to evaluate the limit. It is also important to pay attention to any restrictions on the domain of the function.

3. Can limits be used to find the value of a function at a certain point?

No, limits cannot be used to find the value of a function at a specific point. They only describe the behavior of the function near that point. To find the value of a function at a certain point, you need to evaluate the function at that point.

4. Why are limits important in mathematics?

Limits are important in mathematics because they help us understand the behavior of functions and sequences, and they are essential in calculus and other branches of mathematics. They also have practical applications in physics, engineering, and other fields.

5. What are some common mistakes to avoid when solving limit problems?

Some common mistakes to avoid when solving limit problems include forgetting to check for any restrictions on the domain of the function, using incorrect rules or techniques, and not simplifying the expression before evaluating the limit. It is also important to pay attention to the signs of terms and to use proper notation when writing out the solution.

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