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Unformatted text preview: LBS 118 CALCULUS I Name: 3—5pm , vi FINAL EXAM Student #:
4/29/02 TA name: USE THE GRAPH SHOWN TO FIND THE LIMITS.
(If_ the limit does not exist, EXPLAIN why it does not exist.) 1. Iim f(x) = x>1 2. lim f(x) = Q
x—> 3 3. 'lim f(x)= x—> 2+ 4. lim f(x)= x—> 00 5. lim f(x)= x—~> +00 EVALUATE THE FOLLOWING LIMITS ALGEBRAICALLY:
(You must SHOW WORK for credit and give EXACT answers.) 5. Iim ix+22 7. Iim gab1” 3. lim x
“>23 x2 “>0. 2x3 “>0 tan3x Find dy/dx FOR THE FOLLOWING FUNCTIONS: 9. _ jCOt X +4 X I 4 < DO NOT SIMPLIFY your answer to this one.
y — 3):
e
.l 10. =4y2+2lnx+2xy X y = X 3 ' 3 X 2 (You MUST show work f0r credit)
11. On what interval(s) is the function DECREASING? 12. On what interval(s) is the function CONCAVE UP? 13. Give the exact VALUES of the RELATIVE EXT REMA and‘teil WHERE THEY OCCUR:
(Make sure you tell which are MINIMA and which are MAXIMA.) 14. Give the exact VALUES of the INFLECTION POINTS and tell WHERE THEY OCCUR: 15. Are there any ABSOLUTE extrema? If so, give both x and yvalues: FIND THE FOLLOWING INTEGRALS: 3 2
16. x :lx8 dx 17. X2+2 dx
x(x +4) x1
2 SOLVE THE STORY PROBLEM. NOTE: Volume of a sphere is V = 4I3’ﬂ" r 3 18. The radius of a balloon is DECREASING at a rate of  2 cm/sec. How fast is the VOLUME
of the balloon changing when the radius is 10 cm? (Make sure to label your answer with units.) GIVEN THE GRAPH SHOWN HERE, SET UP THE INTEGRALS BELOW. CURVE I:/y=x+4
CURVE ll: x=1 DO NOT EVALUATE THE INTEGRALS... SET UP ONLY. 19. An integral with respect to X that gives the AREA of the shaded region. 20. An integral which gives the VOLUME generated when rotating the shaded region
around the YAXIS using DISKS or WASHERS. 21. An integral which gives the VOLUME generated when rotating the shaded region
around the X—AXIS using CYLINDRICAL’SHELLS. 22. An integral which gives the VOLUME generated when rotating the shaded region
around the X—AXIS using DISKS or WASHERS. BONUS PROBLEM: (Show work below.) YOU MUST SHOW WORK BY HAND FOR CREDIT. EVALUATE the integral in #2l . and #22 to show that they are EQUAL. ...
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This note was uploaded on 03/19/2008 for the course LBS 118 taught by Professor Nichols during the Winter '01 term at Michigan State University.
 Winter '01
 nichols

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