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Worksheet 7 1.) Initially, a flock of blackbirds numbers 750 in December 1988. Two
years later there are 1000 blackbirds. How many blackbirds will there be
in December 1995 if the rate at which the number of birds changes is
proportional to the number of birds present ? 2.) What definite integral is closely approximated by each of the
following sums ? a) i Ll+ gag . O % £3 (AJAX-L - 7mm) bl w '0 c) g .5. Q d) E00 L:3oo (‘00) I ‘00 . 'LZISOI 500 3.) a.) Let f(x)=3. i. Sketch the graph of f. i
ii. Evaluate J0f(x)dx. 3 for 0 5 x <1
6 for x=1
i. Sketch the graph off . 1
ii. Evaluate Jo f(x)dx. b.) Let f(x): i 0.) Let f(x) = " the first digit in the decimal expansion of x " for x in
[0, 1] . For example, f(0.713) = 7 and f(1/3) = 3 . \J i. Sketch the graph of f. i ii. Evaluate I f(x)dx.
o 4.) Asume that y is a differentiable function of x, and compute
y ' = dy/dx for each of the following. 7 - ex
a.) y = IO ex9 dx b.) y =10 arctanx/Tdt
c.) y=,[ (t2+5)10dt d.) y2x+cos(3y)=tan2x
e.) I [7+cos(t2)] dt=lny-x5
a) 3 33 b) 3—,“er M
c) X M d) 3 xi M
l—er‘l “l' [+X1
9) X3 f ‘
Sl+xl M ) Ski-PX;
g) g (“01 M h.) S (“01 M
I) SCXHV M J) Smﬁwl M
k) M I) S I”)? M m.) S UMX)1M n_) SX‘MX M X
0') 8x lynx M p') S x('7\+ﬂmx)'
q') 8 4? ghtmmpw q I x'“ dx
5.) JR.In(x3) dx t.) Jlmf? dx
u.) I (lnx)2 dx . ,v.) I xe-x dx
w.) I arctanx dx x.) I sin I)? dx
y.) IeW‘dx z.) I Xx}??? dx 6.) Let S(x) be the square of the distance from (O, O) to the point (x, y)
on the graph of y = e x . Compute the average value of S for x in [0, 2] . ...
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This note was uploaded on 12/01/2010 for the course MAT 21B MAT 21B taught by Professor Mat21b during the Winter '07 term at UC Davis.
- Winter '07