we r given that the curves y =integation from -infinity to x f(t)dt through the point (0,1/2) and y=f(x),where f(x)>0 and f(x) is differntiable for x belongs to R through (0,1).If tangents dranw to both the curves at the point having equal abscissae intersect on the same point on x axis then 


no. of solutions f(x)=2ex = ?

2 years ago

Share

Answers : (2)

                    

hey,this question is in the GRAND MASTERS PACKAGE.Have you completed all the questions of GMP?

2 years ago
                    

From the first relation,


 


dy/dx = f(x)


Equation of tangent at (0,1/2):


 


(y-0.5)/(x-0) = f(x)


or, x.f(x) = y-1/2


 


From the second relation,


 


dy/dx = d(f(x))


 


Equation of tangent at (0,1):


 


(y-1)/(x) = d(f(x))


 


x.d(f(x)) = y-1


 


Note (0,1/2) and (0,1) has same abscissae, so,


On the x-axis, let the common point be (h,0)


Both the equations should satisfy this point.


 


h.f(h) = -0.5          ............(i)


h.d(f(h)) = -1           ...........(ii)


 


dividing (i) and (ii),


 


d(f(h))/f(h) = 2


Integrating both sides,


 


ln (f(h)) = 2h + c


f(h) = e^(2h+c)


 


the function is f(x)=e^(2x+c)


 


Given the y=f(x) passes through (0,1), putting the values, in the above relation,


 


1 = e^(c)


or, c = 0


 


therefore the funtion is, f(x) = e^(2x)


 


 


Now,


 


f(x) = 2e^(x)


or, e^(2x) = 2.e^(x)


or, e^(x) = 2


or, x = ln2


 


so, i get just one solution. And i m really curious to know the answer. :) ..

2 years ago

Post Your Answer

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
x square + 1 / x square -1 whole root
 
 
first of all separate as( x/x-1)+ (1/x-1)...okay...then integrate separately by taking x-1=t.. then on intgration dx=dt put it... and where there is x in numerator take x=t+1 since, x-1=t...
 
Shyam Chand 5 months ago
 
just simplify as [(x+1)/(x-1)]x[(x-1)/(x-1)] you will get simple eqn to remove under root
 
Shyam Chand 5 months ago
WHat is the integration of a x /b x?
 
 
Integral : (a/b)^x / log(a/b)Thanks Bharat BajajIIT Delhi askiitians faculty
  img
bharat bajaj one month ago
 
Hello Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar one month ago
 
Thanks Bharat BajajIIT Delhi askiitians faculty
  img
bharat bajaj one month ago
integrate 1/(a+bcosx)^2 dx
 
 
Ans: Now, simply use the standard form & partial farction
  img
Jitender Singh 5 days ago
Juliet has attempted 213 problems on Brilliant and solved 210 of them correctly. Her friend Romeo has just joined Brilliant, and has attempted 4 problems and solved 2 correctly. From now on,...
 
 
solution: for minimum no. of probs for rotio of correct solutions to attempted probs.. R's ratio > J's ratio. assume X problems are attempted by both and R does all correctly and J does...
  img
Ajay Verma 4 months ago
 
method was right but its not a right answer.
 
shubham jain 4 months ago
 
then what is the correct answer?
 
Ketan Jain 4 months ago
If the sum of distances of a point from two perp[endicular lines in a plane is 1, the find the locus of the point.
 
 
Ans: Line Sol: Let the coordinates of the point be (h, k). The equation of two perpendicular lines: ….......(1) …...........(2) Whera a, b, c & c ’ are constants. Let...
  img
Jitender Singh one month ago
"a relation R is defined from a set A={2,3,4,5} to a set B={3,6,7,10} as follow:"(x,y) belong to R and x is relatively prime to y . determine its range and domain“
 
 
according to given relation , (x,y) belong to R and x is relatively prime to y . determine its range and domain“ for x=2 , y= 3,7 x=3, y= 4,5 x=4 , y=3,5 x=5 , y= 2,3,4
  img
Sher Mohammad 8 days ago
View all Questions »