Guest

In Differential Calculus by Arihant Publication Pg.no. 88 - Q.no. 2,3,5 Pg.no. 90 - Q.no. 15,17 Pg.no. 91 - Q.no. 29 FOR THOSE WHO DONT HAVE THIS BOOK: NOTE: D is same as (d/dx) f(-1)(x) is same as f inverse of x ^3 means 'power 3' 'pi' is same as 22/7 or 3.14 'sqrt.' is same as square root of 1) Let f(x) = (2x-pi)^3 + 2x - cosx. The value of D(f(-1)(x)) at x = pi is: a) 3 pi^2 + 2 b) -2 c) 1/(3pi^2 + 2) d) 1/3 2) A function f:R->R satisfies sinx cosy (f(2x+2y) - f(2x-2y)) = cosx siny (f(2x+2y) + f(2x- 2y)). If f'(0)=1/2, then: a) f''(x) - f'(x) =0 b) 4f''(x) + f(x) =0 c) f''(x) + f(x) =0 d) 4f''(x) - f(x) =0 3. If y= sec(-1)((x-1)/(x+1)) + sin(-1)((x-1)/(x+1)), then Dx=? a) 1 b) 0 c) (x-1)/(x+1) d) (x+1)/(x-1) 4. If sqrt.(x^2 + y^2) = a e^(tan(-1)(y/x)), a>0 then y''(0) is: a)(a/2) e^(-pi/2) b) a e^(pi/2) c)(-2 e^(-pi/2))/a d) does not exist 5. If P(x) is a polynomial such that P(x^2+1)={P(x)}^2 + 1 and P(0)=0 then P'(0) is equal to: a) 1 b)0 c) -1 d)none of these 6)Let f:R->R be a differential function satisfying f(y).f(x-y)=f(x) for all x,y and f'(5)=q and p.f(0)=f'(0) then f(5) is: a) p^2/q b) p/q c) q/p d) q. Please help me askIITians.

 In Differential Calculus by Arihant Publication 
Pg.no. 88 - Q.no. 2,3,5
Pg.no. 90 - Q.no. 15,17
Pg.no. 91 - Q.no. 29

FOR THOSE WHO DONT HAVE THIS BOOK:
NOTE:
D is same as (d/dx)
f(-1)(x) is same as f inverse of x
^3 means 'power 3'
'pi' is same as 22/7 or 3.14
'sqrt.' is same as square root of 


 


1) Let f(x) = (2x-pi)^3 + 2x - cosx. The value of D(f(-1)(x)) at x = pi is: 
  a) 3 pi^2 + 2
  b) -2
  c) 1/(3pi^2 + 2)
  d) 1/3

2) A function f:R->R satisfies 
  sinx cosy (f(2x+2y) - f(2x-2y)) = cosx siny (f(2x+2y) + f(2x-   2y)).  If f'(0)=1/2, then:
  a) f''(x) - f'(x) =0
  b) 4f''(x) + f(x) =0
  c) f''(x) + f(x) =0
  d) 4f''(x) - f(x) =0

3. If y= sec(-1)((x-1)/(x+1)) + sin(-1)((x-1)/(x+1)), then Dx=?
  a) 1                     b) 0
  c) (x-1)/(x+1)       d) (x+1)/(x-1)

4. If sqrt.(x^2 + y^2) = a e^(tan(-1)(y/x)), a>0 then y''(0) is:
   a)(a/2) e^(-pi/2)               b) a e^(pi/2)
   c)(-2 e^(-pi/2))/a              d) does not exist

5. If P(x) is a polynomial such that P(x^2+1)={P(x)}^2 + 1 and P(0)=0 then P'(0) is equal to:
   a) 1                  b)0
   c) -1                 d)none of these

6)Let f:R->R be a differential function satisfying           f(y).f(x-y)=f(x) for all x,y and f'(5)=q and p.f(0)=f'(0) then f(5) is:
  a) p^2/q               b) p/q
  c) q/p                   d) q.

Please help me askIITians. 


   

 

Grade:12

1 Answers

Aman Bansal
592 Points
11 years ago

Dear Abhishek,

1) It's "pi". (2) pi is _not_ 22/7

Now that that's over with, first find 

df(x)/dx = 3(2x - pi)^2 * 2 + 2 + sin(x)

Let x = pi to get 3*pi^2 * 2 + 2 + 0 = 6pi^2 + 2

So the answer is | 1 / (6pi^2 + 2) | = 1 / (6pi^2 + 2)

Best Of Luck...!!!!

Cracking IIT just got more exciting,It’s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and winexciting gifts by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple click here to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free