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1. (1 point) . . . . f (x) g(x) The graphs of f(x) and g(x) are given above. Use them to eval- . uate each quantity below. Write DNE if the limit or value does not exist (or if it's infinity). . 1. lim If(x)g(x)] * + 0+ 2. lim If(8(x))] . * - 0- 3. lim If(x) +8(x)] * -+ 2 + . 4. f(2)8 (2) 5. lim If(x)/8(x)] (incorrect) 6. lim [f(x)/8(x)] 2. (1 point) x-+ 2 For the function f whose graph is given, state the value of the 7. lim If(8(x) )] * - 2 - given quantity, if it exists. If it does not exist, enter "n" below. 8. lim If (8(x))] (a) lim f(x) X -+ 2+ X-+0 9. f(0) + 8(0) (b) lim f(x) 10. f(8(0) ) * -+ 3 - (c) lim f(x) 11. lim [f(x)/8(x)] * + 3 + * -+ 2 + (d) lim f (x) 12. lim [f(x)/8(x)] X-+3 X - 0- (e) f(3) 13. f(0) / 8(0) 14. f(g(2)) 15. f(0) 8 (0) 16. lim If(8(x) )] x -+ 0+ 17. lim [f(x) + 8(x)] x -+ 2 - 18 . f ( 2 ) + 8 (2 ) 19. lim [f(x) +8(x)] (a) * - 0- (b) 20. lim [f(x)g(x)] (c ) x -+ 0- 21. lim [f(x) + 8(x)] (d ) x-0+ (e) 22. f(2) /8( 2) 23. lim If(x)g(x)] Answer(s) submitted: * -+ 2 - 24. lim If(x)g(x)] x -2+ Answer(s) submitted:(incorrect) 3. (1 point) The point P(25,8) lies on the curve y : (/3 + 3. Let Q be the point (x, J} + 3). 3.) Find the slope of the secant line PQ for the following values of 3:. (Answers here should be correct to at least 6 places after the decimal point.) If x = 25.1, the slope of PQ is: If x : 25.01, the slope ofPQ is: If x : 24.9, the slope of PQ is: If x = 24.99, the slope of PQ is: b.) Based on the above results, estimate the slope of the tangent line to the curve at P(25, 8). Answer: Answer\") submitted: (incorrect) 4. (1 point) A function is said to have a horizontal asymptote if either the limit at innity exists or the limit at negative innity exists. Show that each of the following functions has a horizontal asymptote by calculating the given limit. 3x ll 12 =_ .32.. +x22x+10 um 613x+ 4x2+13 , x) 12+x (2x13)27 1i 2x+15 14x127 reex15 x9 _ limVx2+l3x4x:_ x)oo lirn x2+13x4+x=_ x470: Answer\") submitted: (incorrect) 5. (1 point) Evaluate the limit, if it exists. If not, enter \"n\" below. . x2 + x 6 11m xal x 2 Answe s ) submitted: (incorrect) 6. (1 point) Evaluate the following limit. If the answer is positive innite, type "I\"; if negative innite, type \"N\"; and if it does not exist, type \"D\". lirn 12r35x+9 JHm 1+2x2+3x3 Answe s ) submitted: (incorrect) 7. (1 point) Let m) = 2x4 +4. (a) Use the limit process to nd the slope of the line tangent to the graph of f at x : 2. Slope at x : 2: (b) Find an equation of the line tangent to the graph of f at x : 2. Tangent line: y = Answerf s ) submitted: (incorrect) 8. (1 point) Evaluate the limit : 1 lim II I. ;>1+ xl If the limit does not exist, enter DNE. Limit = Answes) submitted: (incorrect) 9. (1 point) \\/3x+5, ifx 4 Calculate the following limits. Enter DNE if the limit does not exist. lim f(x) : x4 74 lim f(x) = _ *-7-4+ (a) lim x-too Vx2 - 3x + 1 -x = lim f(x) = Answer(s) submitted: (b) lim Vx2 - 3x + 1 - x) = (incorrect) Answer(s) submitted: 10. (1 point) Evaluate the following limits. If needed, enter INF for co and MINF for -co. (incorrect)
