Typical application of Green's Theorem (1)

Linjing Guo published on 2021-12-31 included in category Calculus

Compute the improper integral by using the polar coordinates

Linjing Guo published on 2021-12-29 included in category Calculus

Different perspectives of a problem involving tangent line

Linjing Guo published on 2021-12-29 included in category A Level Math

Double integral on the elliptical region

Linjing Guo published on 2021-12-07 included in category Calculus

Double integral on the circular region

Linjing Guo published on 2021-12-07 included in category Calculus

An Example for the Nature of Critical Points of Multi-variable Functions

Linjing Guo published on 2021-12-06 included in category Calculus

One Exercise about Lagrange Multiplier

Linjing Guo published on 2021-12-04 included in category Calculus

Three different solutions to one problem.

Question

The temperature at a point $(x,y)$ on a metallic floor is $T(x,y)=4x^2-4xy+y^2$. Wearing thermocouples shoes that measures temperature, you walk along a circle of radius $5$ centered at the origin on the metallic floor. What are the highest and lowest temperatures measured by your shoes?

~~~~~*~~~~~*~~~~~*~~~~~