Limits and Continuity/Partial Derivatives
Limits and Continuity/Partial Derivatives
Christopher Croke
University of Pennsylvania
Math 115
Christopher Croke
Calculus 115
Limits
For (x0, y0) an interior or a boundary point of the domain of a function f (x, y ). Definition:
lim f (x, y ) = L
(x,y )(x0,y0)
if for every > 0 there is a > 0 such that: for all (x, y ) in the domain of f if
0 < (x - x0)2 + (y - y0)2 <
then |f (x, y ) - L| < .
Christopher Croke
Calculus 115
Limits
For (x0, y0) an interior or a boundary point of the domain of a function f (x, y ). Definition:
lim f (x, y ) = L
(x,y )(x0,y0)
if for every > 0 there is a > 0 such that: for all (x, y ) in the domain of f if
0 < (x - x0)2 + (y - y0)2 <
then |f (x, y ) - L| < .
Christopher Croke
Calculus 115
This definition is really the same as in one dimension and so satisfies the same rules with respect to +, -, ?, ?. See for example page 803 for a list.
Christopher Croke
Calculus 115
This definition is really the same as in one dimension and so
satisfies the same rules with respect to +, -, ?, ?. See for
example page 803 for a list.
For example:
if
lim f (x, y ) = L and lim g (x, y ) = K
(x,y )(x0,y0)
(x,y )(x0,y0)
Christopher Croke
Calculus 115
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- solution 7 university of california berkeley
- solving des by separation of variables
- 5 introduction to harmonic functions
- unit 5 implicit di erentiation related rates implicit
- 5 2 limits and continuity
- covariance and correlation math 217 probability and
- review for exam 2 section 14 michigan state university
- limits and continuity partial derivatives
- chapter 4 jointly distributed random variables
- first examples ucsd mathematics home
Related searches
- derivatives of exponents and logs
- derivatives of logarithms and exponents
- second order partial derivatives calc
- four second partial derivatives calculator
- second partial derivatives calculator
- find the partial derivatives calculator
- partial derivatives khan academy
- partial derivatives explained
- limits and continuity calculator
- partial derivatives multivariable calculator
- second order partial derivatives calculator
- partial derivatives multivariable