Sheet2 - Math 21B Kouba Challenge Sheet 2 n 3‘ 1 1...

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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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