1. I.T./Sem-1
Nisha Lathiya
Enroll. No. 140210116032
Government Engineering
College Bhavnagar.

2. Calculus
 Partial
Differentiation
 Limits
 Continuity
 Partial Derivatives
of a Function
 Higher order
derivatives
 Applications

3. Limits
 Definition :
 If given any number ε >0
 |f(x,y-L)| < ε
 Whenever (x,y) lies in the domain of f and
 0<√(x-x0)²+(y-y0)² < ∂
 Then we say that limit of f9x,y0 is L as (x,y)
approaches (x0,y0) and we shall write
 Lim f(x,y)= L
 (x,y)->(0,0)

4. Continuity
 The function u=f(x,y) is said to be continuity at
the pit (a,b), if for all points (x,y) near (a,b) the
value off9x,y) differs, but little , from the value
f(a,b).
 In other wods, if f has the domain R and
Q=(a,b) is a point of R, then f is Continuous at
Q if for every ε>0 there exist a ∂ such that
 |f(P)-f(Q)|=|f(x,y)-f(a,b)|< ∂…………

5. Continuity
………………For all P=(xy) in R for
which
 PQ=√(x-a)²+(y-b)²< ∂
 If a function is continuous at every
point of a domain R, w say that it is
continuous in R.

6. Partial Derivatives of a function
U=f(x0,y0)

7. Partial derivatives of a function
 Assuming that the function u=f(x,y) is defined
at the point (x0,y0), if we differentiate the
function u=F9xo,yo0 at the point x=x0 we btain
the partial derivative of f(x,y) with respect to x
at the point (x0,y0) :
 Lim
h->0

8. Thank You