**Unformatted text preview: **Math 21B
Kouba
Challenge Sheet 2 n 3‘ 1
1.) Convert lim 2 (2 + l) — to a deﬁnite integral and then evaluate it using the Funda—
n—>oo i—l T], 7'], mental Theorem of—Calculus. Choose the general sampling point to be 3’ 3'
b.)ci:—Z c.)ci=2+—Z z
a.) (21-: —
n n n 4
2.) Assume that f is an even function and / f ($) dm 2 5 . Evaluate
0 a.) [gnaw b.) /O—4(2—f(:n))d:r 2
3.) Assume that f is an odd function and / f(a:) dm : —4 . Evaluate
0 0 1
a.)/ (5+f(m))dm b)/ (f(a:))3dz _2 ~1 4.) Determine the x-values for all relative maxima and minima on the interval [—3, 2] for the
following function : F(:C) 2 /3D t(t — 1)5(t + 2)2dt —1
1
5.) Use the limit deﬁnition of a deﬁnite integral to evaluate / 10$ dx.
0 6.) Use any method to evaluate the following definite integral : (1/3)log 1000
/ sin3 a: - cosg(2x) da:
1 7.) Assume that lengths A and B and
angle a are given. Determine the value
of the circle’s radius r in terms of A, B,
and a. ...

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- Winter '09
- Kouba
- Calculus