Midterm 1 3 Practice 5 Midterm True/False For each of the following questions respond true if the statement is true and false if the statement is false. If your response is false give a counter example or explain why. 1. It is possible for the sum of infinitely many numbers to converge. r o.. etç*_ Sv 2. A Riemanu sum with a finite partition is exactly equal to the corre sponding definite integral. i 6 =;) c 3. ff(z)dx = ff(x)dx - I J rwr 4 a.. C-. 4. For an increasing function the left Riernann sum method always over estimates the definite integral. d?-.’\-Q tr3 1 F\ iVckf1y C ID __f_( j ff(x)di. 6 a a 1i-.p 5 woiA j, 0v iw + _ o Free response 2 1. Evaluate the following sum: 7 • (kiT Z k sin() (-if I + a (!!) S—(1T’) •i k-- I •W “\ - O -3 2. Represent the following S=1+3+5+7+. ...+1ö 8 O1Q. 2 (r’) , -4-O— O sum in -C(f1\ 6r Sigma notation and then evaluate it: Q) -. - 8 zz 1-:. i 0 2 LI 3. Use the Riemann Sum definition of the definite integral to evaluate 3 J’(2x + 4)dx 3 0 z (i? ‘-4 - L!2J ‘ci 0 > ‘I C) 3 ELIi —i, 4: ((‘) I ( —.t \. r) I + 9 44 . F9 I8 n )i%Y-l) 2 V.’ C’ 4— n 4- Cl, V.-’ - 4. If the velocity function of an object starting at the origin is given as f 2t :te[0,5] 10 :E[5,oo) Find the location of the object at t=20 and at t50. 0 ID 0 ÷ S. [ink] 5 (Io c (‘&) cH + - L 2 (—o) • J -= 4 to.) V II .1’ II -J. -v -4 .1 3 0 II A - -7 -Y c A A IA - ii (I 0 4_. - ‘4 A A -4 A — -0 I_4 + Ii-ri-I ( H II -‘4 cl A S -4- F F- -;- -4- •1. %1 -- - — .4 ‘4 ___ + Ii Go C. C, (yr ST) ‘I “-I LP. (J C ÷ LY ‘3 a I’ 1 TI I’ ° U Ui 5L? 01 + CD CD CD CD 0 \Il\ , C C Im __ c C -1—- I! a 92 II £ c p ‘I ¶ p CD— + CD CD E CD CD CD O x ‘1, 0 U _\ 1 0 ‘1< _\ci -‘0 0 , 0 C V) ,— It v7 0 0 S 9) - - Q C U) ÷ C -II — 0 — r7 C — Cl 0 rTh ‘I _\r6 _j3 — U I’ U I— I,— c) U 0 4