代写MATH 237 Online Calculus 3 for Honours Mathematics Spring 2024 Mini-midterm 1代写C/C++程序

MATH 237 Online Calculus 3 for Honours Mathematics

Spring 2024

Mini-midterm 1

Due date: 11pm, May 31 2024

1.(40 points) Evaluate the limit or show the limit does not exist.

(i) (15 points)

(ii) (15 points)

(iii) (10 points) Suppose a, b, c, d are positive numbers and a Find

2.(30 points) Suppose

(i) Find the gradient of f.

(ii) Find the linear approximation at the point (0, 25, 1)

(iii) Use the linear approximation above to estimate

3.(20 points) Suppose

(i) (5 points) Is fpx, yq continuous at p0, 0q?

(ii) (10 points) Calculate fxyp0, 0q and fyxp0, 0q.

(iii) (5 points) State Clairaut’s Theorem. Discuss why (ii) is not contradictive to Clairaut’s Theorem.

4.(10 points) Suppose fpx, yq is bounded on the disk

Moreover, f is homogeneous with order i.e.,

Find