Differential Equations

Question 1

Writing limits of multivariable functions

Answer 1

Lim(x,y)→(a,b) for f

Question 2

Boundry point

Answer 2

Any point that exists on the border of a set of points that meet a multivariable equation

Question 3

Interior point

Answer 3

Point that exists within the set of points that fit the multivariable equation

Question 4

Open set

Answer 4

A set of only interior points

Question 5

Closed sets

Answer 5

A set of points that include all boundary points for a multivariable equation

Question 6

2 path test

Answer 6

If there are two paths to the (x,y) point, the limit does not exist

Question 7

Partial derivatives for x-value

Answer 7

Lim(h→0) [f(a+h,b)-f(a,b)]/h

Question 8

Partial derivatives for y-value

Answer 8

Lim(h→0) [f(a+h,b)-f(a,b)]/h

Question 9

Higher order Derivatives

Answer 9

J

Question 10

Differentiable points on a region

Answer 10

Of a function is differentiable at one point, its differentiable at all points

Question 11

Chain Rule (One independent Variable)

Answer 11

H

Question 12

Chain Rule (Two independent Variables)

Answer 12

S

Question 13

Implicit Differentiation

Answer 13

dy/dx=-F(x)/F(y)

Question 14

Directional Derivative

Answer 14

Lim(h→0) (f(a+hcosθ,b+hsinθ)-f(a,b))/h

Question 15

Check for extrema in surfaces using differtial equations

Answer 15

P

Question 16

Euler’s method for differential equations

Answer 16

D