0

ADNAN MUHAMMED

Grade 12,

Courses New

Show that the line x/a+y/b=1, touches the curve y=b×e^-x/a at the point where the curve intersect the axis of y.

Show that the line x/a+y/b=1, touches the curve y=b×e^-x/a at the point where the curve intersect   the axis of y.
 

Grade:12

1 Answers

Arun
25750 Points
5 years ago
The curve cuts the y-axis where x=0, so at the point P(0,b). 
The tangent to the curve has slope 
dy/dx=-(b/a)e^(-x/a) =-(b/a) at P. 
The equation of this tangent is (y-b)=(-b/a)x 
which , dividing by b gives y/b - 1 = (-1/a)x 
giving x/a+y/b=1 and this is the given line. 
So the result has been shown.

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More