Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
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 = ?
hey,this question is in the GRAND MASTERS PACKAGE.Have you completed all the questions of GMP?
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. :) ..
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !