, for -1<x<1,prove that =
It is given that
⇒
squaring both sides, we obtain x2(1+y)=y2(1+x)
⇒ x2+x2y=y2+xy2
⇒ x2-y2=xy2-x2y
⇒ x2-y2=xy(y-x)
⇒ (x+y)(x-y)=xy(y-x)
∴x+y=-xy
⇒ (1+x)y=-x
⇒ y=-x/(1+x)
Differentiating both sides with respect to x, we obtain
=
Hence, it proved.
A certain reaction is 50 complete in 20 minutes at 300 K and the same reaction is 50 complete in 5 minutes at 350 K. Calculate the activation energy if it is a first order reaction. Given:
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.