Sol 06 T2 A

A SOLUTIONS to Test 2 11.06.07

l.Find the limits:    a) lim

fO\$D

**>o ^A

b) i™/= Ufo e⁷'^ J ^ę •^U,,y) ’⁽⁰"°

2.    Find the intervals of concavity and the inflectionpoints of f(x) = — x + —x -3x.

■[MMI

f>»x^Ł+ * -6 'Ąęzif AzMZ^-P? EJSp||§    ’

, f , I ftf*. O ,    §jx e c-3-e;'ⁿ “

f"(x) >0 , Łomoe^ f cw Xc    *

_t x - '3 _y £ un f le cU.o i* p oiVJ_s

3.    Compute the 2-nd degree Taylor polynomial and the remainder term for f(x) = —- at

VI-x

point a = 0 and estiipate the value of

f(»M

WY'

A

W-S

*SMR

SS9'\

nft' ffcźź ^% i' i- -(® od

4. Calculate the area of the region bounded by the curves: y = x² and y-2x^:-x.

_ A

' 5

V-2a--o b--l ^Ai ( 'j * ^d' - ^ • T ' — I

*(/-0--O    T»    °

5.    Find the volume of the solid of revolution obtaincd by revolving the region bounded by y = x³ , x = 0 and y = 8 around the x-axis.

^    . rjv*,«m

^    ^v    mH '    < o ■■

6. Write out the form of the partial fractions expansion of the rational function R(x). Do not determine the numerical values of the coefficients.

R(x)-    ²    -

X'5-

7< ^

x²(x -2)(x + 4)

7. Find the following antiderivatives:

, r 2x .    (

^a ^(x²+8)⁷    )

djt = #/< V.?

b) jlHB*)dx- S HłO=    ClA-^-z

i