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

asked in Calculus by Boss (8.3k points)   | 44 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 (10.5k points)  

Related questions

0 votes
1 answer
1
asked in Calculus by Anmol Verma Junior (785 points)   | 81 views
+2 votes
2 answers
2
asked in Calculus by Himanshu Goyal (327 points)   | 126 views
0 votes
1 answer
3
Top Users Jan 2017
  1. Debashish Deka

    8280 Points

  2. sudsho

    5042 Points

  3. Habibkhan

    4716 Points

  4. Vijay Thakur

    4468 Points

  5. Bikram

    4368 Points

  6. saurabh rai

    4212 Points

  7. Arjun

    4052 Points

  8. santhoshdevulapally

    3732 Points

  9. GateSet

    3312 Points

  10. Sushant Gokhale

    3306 Points

Monthly Topper: Rs. 500 gift card

19,138 questions
24,046 answers
52,772 comments
20,283 users