Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve any point (x, y) is
Given: Slope of the tangent is
Slope of tangent of a curve
Integrate
Use partial fraction for
Equate the numerator
Put x=0
A=1
Put x=-1
B=-1
Hence
Hence equation (a) becomes,
Now it is given that the curve is passing through (1,0)
Hence (1,0) will satisfy the equation (b)
Put x=1 and y=0 in b
When we put y=0 in equation b the result is which is undefined
hence, we must simplify equation (b) further
using loga-logb=loga/b
Constant c must be taken as log c to eliminate undefined elements in the
equation.(log cand not any other terms because taking logc completely
eliminates the log terms and we don't have to worry about undefined terms
in the equation)
Eliminate log
Substitute x=1 and y=0
c=-2
put back c=-2 in (c)