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Unformatted text preview: Sample Problems for Midterm I MAT 21B 1)(True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a:
3 (k)2 =
k=1 -1 k=-3 k2
b a b: If f (t) is a continuous function, then c: tan(/3) = 3 d: e:
b a f (t)dt exists. f (x) + g(x)dx = b a f (x)dx +
3 b a g(x)dx
-1 k=-3 3(k)2 = 3
k=1 k2 2) (8 points) Find the antiderivatives of the following functions: a: cost b: c:
3 x3 5 7 x 7 t d: e 3) (6 points) If a ball is thrown upward at a velocity of 20 ft/s. How high will it go? 1 4) (10 Points) Not using the Fundamental Theorem of Calculus, i.e., using Riemann sums, do the following: Decide whether or not the integral exists. If it does, find its value. Show all your work.
1 0 2x - 3dx 5) (8 points) Using the Fundamental Theorem of Calculus (part II), find the following definite integrals: a: b: c: d:
/2 costdx 0 3 3 2 x3 dx 5 5 7 2 7 xdx 2 t 1 e dt 6) (8 points) Find the following integrals, if they exist. (You may use whatever you know, but show your work.) a: b: esint costdt
secztanz dx secz 2 ...
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This note was uploaded on 04/16/2008 for the course MATH 21B taught by Professor Vershynin during the Spring '08 term at UC Davis.
- Spring '08