{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Disc3 - Math 17C Kouba Discussion Sheet 3 1 Find the Jacobi...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 17C Kouba Discussion Sheet 3 1.) Find the Jacobi Matrix for each function. a.) rm) = (3””+4y) 2:1: — 5y b.) may) = ( 1:2: in) c) ﬂaw) = d) f (:6, y) = (COEESELQ e) may) = 2.) Find the linearization L(w) of f (M) 2 (ﬂag?!) at (1:1). a.) Compute f(0.9, —1.2) and L(0.9, —1.2). What do you conclude ? b.) Compute f(3, 2) and L(3, 2). What do you conclude ? d 3.) Assume that z = :vzy + 563/2, 3; = t3, and y = Compute 67: when t = 1 . 4.) Assume that z = ln(a;y) + 6296+”, a: = f(t), and y 2 g(t). If f(0) : —1, f’(0) = 2, (1 9(0) 2 3, and g’(0) = 1 , then what is the value of 67: when t = O ? 5.) A Madagascar hissing cockroach is walking on the plane :v + 2y + 32 = 6 above the circle \$2 +312 2 1. Assume that the roach’s position (ac, y, 2) (distance measured in inches) at time t seconds is determined by a: 2 cost and y = sin 15. Determine the roach’s rate of dz change of elevation ) when t = 0 seconds; t = 7r seconds. Y‘oqchls pa‘l‘h in 15+ oc‘l’ah't‘ 6.) Compute the derivative of f(;r, y) = ln(2;r +3y) at the point P = (2, 0) in the direction of vector A = . 7.) Consider the function f (513,14) = 333/3 and the point P = (2,1) . Determine all unit vectors u so that D?f(2, 1) is a.) as large as possible (f increases most rapidly). b.) as small as possible (f decreases most rapidly). c.) equal to zero. (1.) equal to 1. 8.) Consider the surface given by x2 + y2 + 22 = 169 and the point P = (3, 4, 12) on the surface. Find equations for a.) the plane tangent to the surface at point P. b.) the line normal (perpendicular) to the surface at point P. 9.) Consider the surface (hyperbolic paraboloid or saddle) given by f (CL‘, y) 2: 33:2 — 23/2 +5 and the point P = (2,3, —1) on the surface. Find equations for a.) the plane tangent to the surface at point P. b.) the line normal (perpendicular) to the surface at point P. 10.) Let f(a:, y) = 1:312 + 23 —— 3y . Use a linearization L(a:) at the point (0,0) to estimate the value of f(0.2, —0.1). 11.) Find and classify critical points as determining relative maximums, relative mini- mums, or saddle points. a.)223m2—6\$y+y2+12\$~16y+1 b.)z=:c2y—a:2—2y2 c.) z :2 1:2 -— 8ln(acy) + y2 d.) z = 3x23) — 6:122 + y3 — 6y2 12.) Find the point on the plane a: + 2y + 32 = 6 nearest the origin. 13.) Determine the dimensions and minimum surface area of a closed rectangular box with volume 8 ft.3 14.) Determine the point on the sphere \$2 + y2 + 22 = 4 which is a.) nearest the point (1, ——1, 1). b.) farthest from the point (1, —1, 1). +++++++++++++++++++++++++++++++++ ” If you judge people, you have no time to love them.” — Mother Teresa ...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern