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TEST 2
I. (IOp) Us*, ihe Taylors Formula for f(x.y) ,f(X.y) �" e2i,+3y to find the quadratic (n «* 2) approximation at the origin (0,0). Estimate the value of
f(0.oi.o.oi) = e°-°s.    Ta/ao)- A* + ^ + f
i"r. At 0.0-Ti-    0.0004
Jc"'5? �ó- 2 4-,, �ó */ e*”^ 1 �ó U
l/    o- .    -i- .
P - 3e '    *
<*« ^ <5"1
2.(1 Op) Sketch the region of integration, reverse the order of integration
�
Ms��
�ż2-tiTT'1 - �ŚJ - HTr^ �
' '6 �Ł    ~~
-�'-M �ó�ó�
*
^ y �Ś I y n - t\*
tt--(*-?y ==>
>    KJ«-1
:L._ °
s~n<?
3.(10p) Find the volume of the region that lies below the graph of f(x,y)_. r-j-
above the region R = {(x.y): 0 S x < 1. 0 S y < x2 }.
and
- A fe �Ś ' 3 V*
�ŚJ - (\r 1)
5
tf* * S/1 V'” -1 p-i
* dv
4. (10p) Evaluate the given integral by changing to polar cord, ff�"�"
r Vx' + y2" d*Cly
R is bounded by the curves : y > 0. x.2-*1)^^^ X2 + y2 <^x.
56 f20
j®]
/ � V
'' K
r x
5. (1 Op) Evaluate the following improper mt.    ax
dJ~_
�
3'-
ti
*1 tv’
1 / L*,