AM2 e 01 2007 TEST2 ENG

TEST 2

1. (IOp) Use the Taylora Formula for f(x,y) ,f(X, y) = e^2M'¹ to find the quadratic (n = 2) approximation at the origin (0,0). Estimate the value of f(0.0l,o.0l) = e°”.    T_a/ao)-    +    +6*2 *1^

|| S e*'⁵3 S=3 I

a

2.(1 Op) Sketch the region of integration, reverae the order of integration . ....    ■    Tx~x    .    -1    J°* Jf(x,yj dv

3~iłx-v* - “J    f x-4” ©o

'    - *4 "A    Iz ’ / X - a - -    ¹

i*

4 - (y -0¹-* (*-*)' =2>    {?■*>'

fc-

?, Ili P W

3.(1 Op) Find the volume of the region that lies belo w the graph of f(X,y) /Jj-above the region R = {(x,y):0sxsl, 0<;ysx²}.

, u*rvf7*7r]^,'^v,=    =

o i * o    o    ®1 :

ki^eU

4. (lOp) Evaluate the given integral by changing to polar cord. ff"7=====e=_=5B_

r V*² +y^ł ^*dy

R is bounded by the curves : y > 0, jd-^yi^gTfy; x² + y² <    .

y: \

tfa cos©

M

°    T^ł‘^r M

f _X3

5. (1 Op) Evaluate the following improper int. |—--dx

o * +3

IBR^

^ UłtS: