MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11
        
 Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help  Pls help 
4 months ago

Answers : (1)

Aditya Gupta
2016 Points
							
f(x)= ∫0 to x g(t)dt
f(-x)= ∫0 to – x g(t)dt
let u= – t
f(-x)= – ∫0 to x g(-u)du= – ∫0 to x g(u)du (since g(u)= g(-u) for it is even)
or f(–x)= –f(x)
g(x)= f(x+5)
g(-x)= f(5 – x)
so f(x+5)= f(5 – x)
replace x by 5 – x
f(10 – x)= f(x)
replace x by 20+x
or f(10 – (20+x))= f(x+20)
f(x+20)= f( – (x+10))= – f(10 – ( – x))= – f( – x)= f(x)
hence f(x)= f(x+20)
now differentiating f(x)= ∫0 to x g(t)dt we get f’(x)= f(x+5).......(1)
diff again f”(x)= f’(x+5)= f(x+10)
again diff f’’’(x)= f’(x+10)= f(x+15)
again f’’’’(x)= f’(x+15)= f(x+20)= f(x)
hence solving f’’’’(x)= f(x) we have
f(x)= ae^x + be^-x + csinx + ecosx. also, f’(x)= ae^x – be^-x + ccosx – esinx. substitute in (1)
ae^x – be^-x + ccosx – esinx = ae^5e^x + be^-5e^-x + csin(x+5) + ecos(x+5) identically
hence a= ae^5 and – b= be^-5 so a=b=0
so f(x)= csinx + ecosx but f(0)=0 so e=0 hence f(x)= csinx
and ccosx= csin(x+5), which can be identically true iff c= 0 hence f(x)= 0 or g(x)= f(x+5)= 0.
since it is given in the ques that g should be non zero, but we have proved it to be 0, hence we deduce that the ques is wrong. 
KINDLY APPROVE :))
 
4 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details