ANS CII 07 Test2

T£ST 2

I. (lOp) Usc the Taylora Formula for f(x,y) ,f(x,y) = e^2x+3y to find the quadratic (n = 2) approximation at the origin (0,0). Estimate the value of

f(0.01,0.01) = e' fol)- K

■= 2

Tj/fto)- 4 + 9* +    +    -ł-6*^ ⁺5 8

2,    fff"4 t O.or f 49,S. o. 0004

,Ł”^Jy

a...

2.(1 Op) Sketch the region of integration, reverse the order of integration 3

- Xi\r-r? * %* '^|X '

H

x-^a=-''Y^,Ł’3 * * 2-

^,'^IW

3.( 1 Op) Find the volume of the region that lies below the graph of f (x_s y ^ __ ^

K^Łr^r’_rf>

-2)^ti'- ^Lł> ^4V-l

h--    u-?)' =>

above the region R = {(x,y): 0 < x <1, 0 < y < x² }.

y    d-y~ - jp* [ ’j_Q '= |

+ 1

and

V. -1

a \ oLfc =

l dJb _

4. (lOp) Evaluate the given integral by changing to polar cord. //-R is bounded by the curv

^R »^x + y? ^Jtcjy

y >0, jtis=yŁiSy; x² + y² <^x.

^xN,*^Ł** i

“ ^# 4    ? jjj <OsQ

i^dBJ

⁽-QaQ

?5>

5. (lOp) Evaluate the following improper int J——- dx

ii— = 4: Urn f 1 s * w-ioo L S. t T ’

^a 'i