math_273_(spring_2009)_practice_test_1

# math_273_(spring_2009)_practice_test_1 - MATH 273 PRACTICE...

This preview shows pages 1–7. Sign up to view the full content.

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

View Full Document

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

View Full Document

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 273 PRACTICE TEST 1 NAME: 1. (10 points). Suppose that z = z(x,y) is a function deﬁned implicitly by the equation 23 + x2 — y2 = 1. Use implicit differentiation to ﬁnd 3—: and 2—3. - .Bz__ z g_ 2 Answenm- Mia-52%- 2. (10 points). Find an equation of the tangent plane to the surface given by the graph of f(:r,,y) = 2:122 + 4y2 — 5 at the point P(1, 41,0). Answer: 4(m — 1) + 2(y — ‘11) — z = O. 3. (10 points). Compute all ﬁrst-order partial derivatives of f(r,s,t) = (1 — r2 — 32 — t2)e'"t. 4. (10 points). Prove that - 2 515?! 5103+y3 does not exist. Hint: ﬁnd two different direction of approach (m,y) —> (0,0) leading to different ”limits”. lim<w,y>~<o‘0) 5.(10 points). Find the equation of the plane passing through the points (3, -1, 2), (8, 2, 4) and (-1, —2, -3). Answer: 13(3: — 3) — 17(y + 1) — 7(2 - 2) = 0 6.(10 points). Find the maximal rate of change of f(m,y) = sin(3m — 4y) at P(§, ﬁ) and the direction in which it occurs. Answer: 5, gi — gj. 7.(10 points). The curve is given by r(t) = 2\/Ei + t2j + tk. Find the unit (length must be 1) tangent vector at the point P corresponding to the value t = 1. Then ﬁnd the equation of the tangent line to the curve at P. Answer: 71§i+72gj+71€k,\$=2+t,y=1+2t,z=1+t. 8. (10 points). In the two-dimensional space, the trajectory of a particle is given by 1 . r0?) = 392593 + Vot, where g 2: 10m/s2, v0 = 2\/§i + 2j. a) Find the time when the particle hits the ground; b) Find the distance d between the origin and the point of impact. (To do this, you would need to determine x—coordinate of the impact point). Answer: a) g, b) 445. 9. (10 points). Find the length of the curve r(t) = ti+ lgtzj + %t3k, 0 S t S 1. Hint: to integrate, represent the quantity under the square root as a complete square. This should be easy. can.» Answer: ...
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