MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 320 off
USE CODE: MOB20

				   

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 = ?

4 years ago

Share

Answers : (2)

										

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

4 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. :) ..

4 years ago

Post Your Answer

Other Related Questions on Integral Calculus

limit of n! where n tends to infinite
 
 
limit of n! where n tends to infinite proof
 
samanu anusha 10 months ago
 
limit of n! where n tends to infinity
 
samanu anusha 10 months ago
 
the value is infinite
 
sri tanish 10 months ago
How to find integration of tan3x.tan2x.tanx.? Is there any easy way to solve it
 
 
use standard identities first and then reduc this to an easy expression eqn. then integearte it. Use, tan(A+B) = (tanA + tanB)/(1 – tanAtanB) tanAtanB = 1 – (tanA + tanB)/tan(A+B) for tan2x ...
 
Vikas TU 4 days ago
Find the indefinite integral of f(x) = (x^2 + 3)/((x^6)*(x^2 + 1)) ?
 
 
the answer is indefinite integral of f(x) = integral of(x^2 + 3)/((x^6)*(x^2 + 1)) -3/5x^5 + 2/3x^3 – 2/x – 2arctanx + c where c is an arbitrary constant
 
SREEKANTH one month ago
 
indefinite integral of f(x) = (x^2 + 3)/((x^6)*(x^2 + 1)) is : => -3/5x^5 + 2/3x^3 – 2/x – 2arctanx + c
 
Vikas TU one month ago
20 PEOPLE , OF WHICH 10 ARE DOCTORS AND 10 ARE ENGINEERS GO IN A MEETING , WHEN THEY COME OUT , THEY FIND THEIR JACKETS JUMBLED UP. WHATS THE PROBABILITY THAT NO ENGINEER GETS HIS ORIGINAL...
 
 
there are 20 coats, so the probability of the first engineer getting his coat wrong is 19/20, as there is only a 1/20 chance of getting the coat correct. the probability of the 2 nd...
 
Dhruva Narayan 5 months ago
If a,b,c be the unit vectors such that b is not parallal to c and a X(2bXc)=b then the angle that a makes with b and c are respectively where (X represents cross product)
 
 
We need to look at only one relation Taking dot product both sides wrt a the LHS will become zero (obviously) hence also now we can expand the given vector triple product as as a.b=0 and...
  img
Riddhish Bhalodia 5 months ago
Write direction ratios of the vector a = i + j − 2k and hence calculate its direction cosines?
 
 
Note that direction ratios a, b, c of a vector r = x i + yj + zk are just the respective components c, y and z of the vector. So, for the given vector, we have a = 1, b=1, c= –2. Further,...
 
KUNCHAM SAMPATH 7 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,000 off
USE CODE: MOB20

Get extra R 320 off
USE CODE: MOB20

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