Set of values of $frac{x^3sinleft(x^3right)}{x^2+2xcos x + 2}$ [closed]
$begingroup$
How to find the set of values of $$f(x)=frac{x^3sin(x^3)}{x^2+2xcos x + 2}?$$
I tried using Taylor series, limiting, comparing and derivation but none of these worked for me. Have you got any tips on how to deal with this issue?
real-analysis functions
edited Jan 16 at 16:03
gt6989b
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
$endgroup$
closed as unclear what you're asking by Nosrati, max_zorn, user91500, Lord_Farin, Cesareo Jan 17 at 9:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
How to find the set of values of $$f(x)=frac{x^3sin(x^3)}{x^2+2xcos x + 2}?$$
I tried using Taylor series, limiting, comparing and derivation but none of these worked for me. Have you got any tips on how to deal with this issue?
real-analysis functions
edited Jan 16 at 16:03
gt6989b
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
$endgroup$
closed as unclear what you're asking by Nosrati, max_zorn, user91500, Lord_Farin, Cesareo Jan 17 at 9:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
How to find the set of values of $$f(x)=frac{x^3sin(x^3)}{x^2+2xcos x + 2}?$$
I tried using Taylor series, limiting, comparing and derivation but none of these worked for me. Have you got any tips on how to deal with this issue?
real-analysis functions
edited Jan 16 at 16:03
gt6989b
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
$endgroup$
How to find the set of values of $$f(x)=frac{x^3sin(x^3)}{x^2+2xcos x + 2}?$$
I tried using Taylor series, limiting, comparing and derivation but none of these worked for me. Have you got any tips on how to deal with this issue?
real-analysis functions
real-analysis functions
edited Jan 16 at 16:03
gt6989b
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
edited Jan 16 at 16:03
gt6989b
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
edited Jan 16 at 16:03
gt6989b
35.5k22557
edited Jan 16 at 16:03
gt6989b
35.5k22557
edited Jan 16 at 16:03
gt6989b
35.5k22557
35.5k22557
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
asked Jan 16 at 15:45
Filip WichrowskiFilip Wichrowski
206
206
closed as unclear what you're asking by Nosrati, max_zorn, user91500, Lord_Farin, Cesareo Jan 17 at 9:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Nosrati, max_zorn, user91500, Lord_Farin, Cesareo Jan 17 at 9:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
HINT
We have
$$
f(x)
= frac{xsin(x^3)}{1+2x^{-1}cos x + 2x^{-2}}
$$
so as $x to infty$, the denominator approaches 1 and the denominator oscillates with linear amplitude, which suggests that the range $f(x)$ is the set of all real numbers.
The intuition is supported by the graph of $f(x)$ over $x in [0,20]$ from Wolfram Alpha:
Can you formally prove it?
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
$endgroup$
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT
We have
$$
f(x)
= frac{xsin(x^3)}{1+2x^{-1}cos x + 2x^{-2}}
$$
so as $x to infty$, the denominator approaches 1 and the denominator oscillates with linear amplitude, which suggests that the range $f(x)$ is the set of all real numbers.
The intuition is supported by the graph of $f(x)$ over $x in [0,20]$ from Wolfram Alpha:
Can you formally prove it?
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
$endgroup$
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
add a comment |
$begingroup$
HINT
We have
$$
f(x)
= frac{xsin(x^3)}{1+2x^{-1}cos x + 2x^{-2}}
$$
so as $x to infty$, the denominator approaches 1 and the denominator oscillates with linear amplitude, which suggests that the range $f(x)$ is the set of all real numbers.
The intuition is supported by the graph of $f(x)$ over $x in [0,20]$ from Wolfram Alpha:
Can you formally prove it?
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
$endgroup$
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
add a comment |
$begingroup$
HINT
We have
$$
f(x)
= frac{xsin(x^3)}{1+2x^{-1}cos x + 2x^{-2}}
$$
so as $x to infty$, the denominator approaches 1 and the denominator oscillates with linear amplitude, which suggests that the range $f(x)$ is the set of all real numbers.
The intuition is supported by the graph of $f(x)$ over $x in [0,20]$ from Wolfram Alpha:
Can you formally prove it?
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
$endgroup$
HINT
We have
$$
f(x)
= frac{xsin(x^3)}{1+2x^{-1}cos x + 2x^{-2}}
$$
so as $x to infty$, the denominator approaches 1 and the denominator oscillates with linear amplitude, which suggests that the range $f(x)$ is the set of all real numbers.
The intuition is supported by the graph of $f(x)$ over $x in [0,20]$ from Wolfram Alpha:
Can you formally prove it?
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
edited Jan 16 at 15:56
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
answered Jan 16 at 15:50
gt6989bgt6989b
35.5k22557
35.5k22557
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
add a comment |
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
Thank you! Yes, I can. But I wonder why my question was downvoted.
$endgroup$
– Filip Wichrowski
Jan 16 at 15:58
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
@FilipWichrowski I did not downvote, but there are many people here who are of the philosophy that you are suppose to exhibit some of your own work even when posting the question. That position is hard to argue with, since this is not supposed to be "we do your homework gor you" kind of site :-). There is a lot of grey area in the matter and some people use it differently than others...
$endgroup$
– gt6989b
Jan 16 at 16:02
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
Of course, I totally agree with this point of view. Nevertheless, I did post an information that I had tried a few methods that probably were not the best ones out there. By the way, it is not my homework. I'm just keen on figuring out math problems.
$endgroup$
– Filip Wichrowski
Jan 16 at 16:05
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
@FilipWichrowski You are preaching to the choice :) I prefer to hint instead of downvoting, except in really obnoxious cases. But I did upvote your question nevertheless. Next time, likely posting some details in the arguments that did not work would help.
$endgroup$
– gt6989b
Jan 16 at 16:11
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
$begingroup$
Sure. Thanks again!
$endgroup$
– Filip Wichrowski
Jan 16 at 16:18
add a comment |
