A 11.06.07

CALCULUS I Test 2

Name in BLOCK CAPITAL LETTERS:……………………………………………..

Task 1 (10p.) Find the limits: a)
b)

Task 2 (5p.) Find the intervals of concavity and the inflection points of

.

Task 3 (5p.) Compute the the 2-nd degree Taylor polynomial and the remainder term for

at point
and estimate the value of
.

Task 4 (5p.) Calculate the area of the region bounded by the curves:

and
.

Task 5 (5p.) Find the volume of the solid of revolution obtained by revolving the region bounded by
,
and
around the x-axis.

Task 6 (5p.) Write out the form of the partial fractions expansion of the rational function R(x). Do not determine the numerical values of the coefficients.

Task 7 (15p.) Find the following antiderivatives

a)
, b)
, c)