GATE CSE
First time here? Checkout the FAQ!
x
0 votes
58 views

asked in Calculus by Boss (8.6k points)   | 58 views
is it option A?
Yes but how?

1 Answer

0 votes

I think this should be the logic.

Let f(x) = $\frac{\cos ^{m}x}{x^{n}}$

Value of x Value of n
<1 <1
<1 >=1
>=1 <1
>=1 >=1

 

Now, we focus for first 2 cases (i.e. x<1 since x has more values less than 1  rather than greter than 1)

 

Now, if we consider n>=1, then consider what will be instantaneous value of f(x).

e.g n=100 and x=0.02

$\therefore$ cosmx<1 but xn$\rightarrow$0

So, instantaneous value is very high and thus, integration of f(x) will never converge.

 

Now, if we consider n<1, then consider what will be instantaneous value of f(x).

e.g  n=0.9  x=0.02

$\therefore$  instantaneous value of f(x) will be finite. (just try taking an example)

So, this will converge.

 

So, my answer was just a calculated guess. I dont know if there is any solution by using the series expansion of cos(x).

 

 

answered by Veteran (14.8k points)  

Related questions

0 votes
2 answers
1
asked in Calculus by sh!va Veteran (24.1k points)   | 30 views
0 votes
2 answers
3
asked in Calculus by sh!va Veteran (24.1k points)   | 24 views


Top Users Mar 2017
  1. rude

    4758 Points

  2. sh!va

    3014 Points

  3. Rahul Jain25

    2830 Points

  4. Kapil

    2636 Points

  5. Debashish Deka

    2450 Points

  6. 2018

    1514 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1314 Points

  9. Bikram

    1286 Points

  10. Sanjay Sharma

    1076 Points

Monthly Topper: Rs. 500 gift card

21,484 questions
26,812 answers
61,056 comments
23,065 users