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Math 232 In-Class Exam Solutions - March 19, 2007 - Prof. Andrew M. Diener, Exams of Advanced Calculus

Christian Brothers University (CBU)Advanced Calculus
Prof. Andrew M. Diener

The solutions to the math 232 in-class exam held on march 19, 2007. The exam covers various topics in multivariable calculus, including finding limits, derivatives, and directional derivatives.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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koofers-user-7qx 🇺🇸

10 documents

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EXAM 2(In Class)
Math 232
March 19, 2007
Name
1. Find the horizontal range and the speed at impact of an ob ject which is launched at an initial
speed of 120 feet per second, 5 feet above the ground, at an angle of π
6radians above the
horizontal. (Assume the only force acting on the object is gravity.) (6 pts)
2. Show that lim
(x,y)→(0,0)
ysin (x)
x2+y2does not exist. (7 pts)
pf3
pf4

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Download Math 232 In-Class Exam Solutions - March 19, 2007 - Prof. Andrew M. Diener and more Exams Advanced Calculus in PDF only on Docsity!

EXAM 2(In Class) Math 232 March 19, 2007

Name

  1. Find the horizontal range and the speed at impact of an object which is launched at an initial speed of 120 feet per second, 5 feet above the ground, at an angle of π 6 radians above the horizontal. (Assume the only force acting on the object is gravity.) (6 pts)
  2. Show that (^) (x,ylim)→(0,0) y sin (x) x^2 + y^2 does not exist. (7 pts)
  1. Determine all the points at which f (x, y) = ln (3 − x^2 + y) is continuous. (6 pts)
  2. Find the linear approximation of f (x, y) = xexy^2 + 3y^2 at the point (2, 0). (6 pts)
  1. Find both ∂f ∂u and^

∂f ∂v for the following function^ z^ = tan

− 1

x y

with x = u^2 + v^2 and y = u^2 − v^2. (8 pts)

  1. Find the directional derivative of f (x, y) = x^2 sin (4y) at the point

− 2 , π 8

in the direction −→u = 〈 2 , − 1 〉. (7 pts)