Assignment 8

Due Monday October 11

12.2 18,19,20

12.3 1,3,4,6

1) a parameterized curve in R² given by

x = t³ y = t⁶

is not differentiable at t = 0.

Sketch the curve. Is it possible to give another parametrization for the same curve which is differential everywhere? If so give such parametrization.

 

2)a canon fire at angle of 30^ƒ. The ball hit the ground 100 ft. from the cannon. assume that the only force is the gravitation (32 ft/sc²) find the initial speed and time of the flight.
 

3) Find the tangential and normal component of the acceleration vector.

a) r(t) = (t2+4)i+(2t-3)j

b) r(t) = ti+4sin(t)j+4cos(t)k

 

4) Drew a couture map of the function showing several level curves.

a) f(x,y) = xy

b ) f(x,y) = exy

c) f(x,y) = x+y x-y

 

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File translated from T_EX by T_TH, version 2.25.
On 7 Oct 1999, 17:28.