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University of British Columbia *
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CHEM 154
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Mathematics
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Apr 3, 2024
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05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 : VVRGEEYYREAL ASSOEYRTN @OF AVERIEN Logged in as Kayla Prabowo. Log Out [ WeBWorK / 2023W1 MATH 100A ALL 2023W1 / Practice Quiz - unlimited time / v1 Gateway Quiz Practice Quiz - unlimited time,v1 Your score on this (checked, not recorded) submission is 21.39/27. The recorded score for this version is 21.39/27. Time taken on test: 245.6 min (39019.5 min allowed). The test (which is version 1) may no longer be submitted for a grade. You may still check your answers. [ Print Test ] Jump to Problem: 1 5 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 2 % Score: 190 (O 100 900 100 50 100 100 900 900 100 900 100 0 0 89 100 100 900 900 900 900 900 100 0 0 4 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 1. (1 point) This is an optional practice quiz that is not for grades. It will be updated throughout the term to pull 25 random "(¥¥¥¥%)" problems from the assignments you have seen so far. You should use this quiz to practice for the first part of the final exam, which will feature 25 questions similar to the ones found here. You may take this quiz an unlimited number of times. A new set of questions will be generated each time you take it. As you might expect from the name, this quiz has no time limit. This is so that you can practice without time pressure, or manually time yourself according to any additional time accommodations that you may have. Please use the "50 minute" version if you wish to practice completing these questions within the time you would be expected to use for this section of the exam during the final. Ok wv 27 120 < preview answers Entered Answer Preview Result Correct Answer Ok Ok correct Ok The answer above is correct. ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 2. (1 point) N ) =1t £ 2 + NV g =¢" » https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ 1715
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 (K ¥ %) Compare the functions f(z) = z11 and g(x) = e® shown in red and blue respectively in the graph above. By zooming in and out, view the functions using several viewing scales. When does the graph of g finally surpass the graph of f? The graphs intersect for the last time at z =~ 1.1057 Hints: You can manually adjust the axes of the graph by clicking on the settings tool in the top right. To get this much accuracy you may need to zoom in very close to the intersection point. You must round your answer or it will be marked wrong. Solution: . (Round your answer to four significant figures.) preview answers ] Entered Answer Preview Result Correct Answer 1.1057 1.1057 The answer above is NOT correct. incorrect ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 3. (1 point) (%% %) Which of the graphs below corresponds to the function g(z) = 523 — 5z* ? (Hint: Consider which power dominates near the origin and which dominates far away from the origin.) e =2 (click on image to enlarge) =2 (click on image to enlarge) https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ 2/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 845 - ® q N o =2 (click on image to enlarge) =2 (click on image to enlarge) O E. None of the above Solution: preview answers Entered Answer Preview Correct Answer D D The answer above is correct. D ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 4. (1 point) (K ¥ 35k) Let the function f be defined by: _Jz4+7 iz <0 f=) = {7 if z > 0. Sketch the graph of this function and find the following limits, if they exist. 1. lim f(z)= 7 2. Iim f(z)- 7 3. lim f(z)= 7 Note: Type INF for co and -INF for —oo. If the limit does not exist, write DNE . Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Correct Answer 7 7 7 7 7 7 https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 3/15
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05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 All of the answers above are correct. ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 5. (1 point) (K ¥%) Suppose g is the y-coordinate of the point of intersection of the graphs below. Complete the statement below in order to correctly describe what happens to g if the value of 8 (in the red graph of g(t) = b(1 + s) below) is increased, and all other quantities remain the same. As s increases, does the value of yg increase, decrease, or remain the same? decrease v Solution: ga—t g{t)=b{1+s)"t f{t)=a{1+r)"t (click on image to enlarge) [ preview answers ] Entered Answer Preview Result Correct Answer DECREASE The answer above is correct. DECREASE correct DECREASE ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 6. (1 point) (k&% %) A ball is thrown straight up into the air with an initial velocity of 22 ft/s. Its height in feet after ¢ seconds is given by y = 22t — 16¢2. Find the average velocity for the time period from ¢ = 3 tot = 3 + h, when h is given as follows: h = .01 sec: 22-32*3.01 h = .005 sec: 22-32*3.005 ft/s h = .002 sec: 22-32*3.002 ft/s h = .001 sec: 22-32*3.001 ft/s https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 4/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 NOTE: For the above answers, you may have to enter quite a lot of significant digits if you are using a calculator. As always, it is recommended you enter your answers in calculator-ready form, and let WeBWorK do the adding/subtracting/multiplying/dividing for you. Note: You can earn partial credit on this problem. preview answers At least one of the answers above is NOT correct. Entered Answer Preview Result Correct Answer -74.32 22 -32-3.01 incorrect —74.1599999999976 -74.16 22 — 32 -3.005 incorrect —74.0800000000006 -74.064 22 — 32 - 3.002 correct —74.0319999999939 -74.032 22 —32-3.001 correct —74.0159999999917 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 7. (1 point) (k¥ %) For the function f(x) shown in the graph below, sketch a graph of the derivative. You will then be picking which of the following is the correct derivative graph, but should be sure to first sketch the derivative yourself. Which of the following graphs is the derivative of f(z)? e \ (Click on a graph to enlarge it,) Solution: N | | I 1 2 3 W 1 2! 3 o preview answers { Entered Answer Preview Result Correct Answer https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ 5/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 8 8 correct 8 The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 8. (1 point) (Kt k) Let f(x) = bx3(x? — 7). Evaluate f(z) at the following points: A) f'(12) = 15*(12)*2((12)*2-7)+10*(12)*4 B) f'(—12) = i15*(-12)'\2((-12)A2-7)+10*(-12)A4 Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Result Correct Answer 503280 15-122(12% — 7) 4+ 10 - 12 correct 3-5-12%(12° —7) +5-12°-2.12 503280 15 - (—12)° ((—12)2 - 7) +10- (-12)* correct 3.5. (—12)2((—12)2 — 7) +5-(-12)%.2. (-12) All of the answers above are correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 9. (1 point) Z (Kedete¥) Let f(z) = i Find f'(z). f' () = | (2X(XA2+4)-2x*x"2)/((x 2+4)"2) Solution: l preview answers ] Entered Answer Preview Result Correct Answer 2z(z? + 4) — 2z z+2—z(1—- %) (2*x*[(xA2)+4]-2*x*(x2))/([(x2)+4] " 2) 3 correct Yy (‘1’2 + 4) (a: + ;) The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 10. (1 point) (Ksesek) Let f(z) = (log(z))*@. Find f'(z). f'(z) = (log(x))M(sec(x))*((secx*tanx*log(logx))+(secx)/(xlogx)) Solution: https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 6/15
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05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 [ preview answers Entered Answer Preview Result Correct Answer ([log ()] [sec(x)])* ([sec()1/Dx*log(X)])] The answer above is correct. z log(z) [sec(*tan()*log(log(x))+ | (log())** (Sec(w) tan(z) log(log(x)) + o) ) correct (Sec(w) tan(z) In(log(x)) + 1:1: %seC(m)) exp(sec(z) In(log(x))) ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 11. (1 point) (¥ % ¥%) Find the derivative of Assume that a and b are constants. W(2) = (-14bATZ)((a+z"2)"8) Solution: [ preview answers ] The answer above is correct. Entered Answer Preview Result Correct Answer [-14*(bAT7)*z]/([a+(z*2)]*8) —14bz 1.77 22( n 2)—1-7—1 4 "Z/([a+( T o8 correct —1-707-2Aa + 2 (a+zz)8 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 12. (1 point) (% %) Find the derivative of the function It may be to your advantage to simplify before differentiating. f'(=) = -sin(sin™(-1)(7x))*(7)/(sart(1-(7x)"2)) f(z) = cos(arcsin(7z)). Solution: preview answers The answer above is correct. Entered Answer Preview Result Correct Answer —sin(sin™'(7z)) - 7 _1.49¢ -si in(7*x))*7 1-[(7*x)A 2 [-sin(asin(7*x))*7)/[sqrt(1-[(7*) A 2))] 1 (72)? correct v1— 492z https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ 7/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 13. (1 point) (¥ ¥ %) Compute the following derivative. % [cos~1(¢/3)] = L(0.25*xM(-3/4))/(sqrt(1-(xA(" |E] Solution: [ preview answers ] Entered Answer Preview Result Correct Answer — (0.2527) g -(0.254[xA -3/ [sqrt(1-([x" (1/4)] 7 2))] - correct J/1- ()2 \/1 - (%) 207 The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 14. (1 point) d (ko) Find d—y by implicit differentiation. T e$5y=m+y dy . —a = (€N(x"5y)"5x"y-1)/(1-x"5) Note: unfortunately, WeBWorK isn't quite smart enough to understand that = + y, for this problem, is the same as eV, After differentiating, don't try to simplify beyond solving for %. Solution: preview answers Entered Answer Preview Result Correct Answer 5 4, z° ey . b5zly —1 : Sz ye® ¥ — 1 e M [(XAS5)Y*Y)*5*(xA4)*y-1]1/[1-(XA5 incorrect (e [OABY YD) *5*(xAAY*y-T1/[1-(xA5)] — P The answer above is NOT correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 15. (1 point) (k%) If fis the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance g from the lens, where f, p, and g are related by the lens equation What is the rate of change of p with respect to q if g = 6 m and f = 7 m? (Make sure you have the correct sign for the rate.) https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 8/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 ap _ ag = | (421312)(6°2) m/s [ preview answers ] Entered Answer Preview Result Correct Answer -(£)° -0.289940828402367 1;” incorrect —49 6 The answer above is NOT correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 16. (1 point) (K ¥ %) Consider the graph of the function f(x) shown below. a) Consider the function at the point 1. f(x1) is[ negative Vv ]' f'(x1) is: positive V] and f"(x1) iS[ negative V]- b) Now consider the function at the point 2. f(z2) is[ positive v], f'(x2) is Zero v] and f"(z2) is[ negative V]- ¢) What is the parity of the function? f(x) iS[ an odd function v ] For the remaining two parts of this question, consider the following 6 graphs. https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 9/15
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05/12/23, 02.15 d) Which is the graph of f'(x)? e) Which is the graph of f"(z)? ¢ \ (Click on a graph to enlarge it) WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 preview answers At least one of the answers above is NOT correct. Entered Answer Preview Result Correct Answer negative negative correct negative positive positive correct positive negative negative correct negative positive positive correct positive zero Zero correct zero negative negative correct negative an odd function an odd function incorrect an even function A A correct A C C correct C ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 17. (1 point) (k¥ ¥ %) Let A be the area of a circle with radius 7 cm. If » is increasing at a constant rate of 5 cm/s then when r = 2 cm, the area A is increasing at a rate of = 20pi preview answers ] { Entered https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ Answer Preview Correct Answer 10/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 62.8318530717959 207 62.8318530717959 The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 18. (1 point) (%% %) Find the linear approximation L(x) of f(z) = logz at # = 1 and use it to estimate log(1.07). L(z) = x-1 log1.07 =~ 0.07 Notice that the linear approximation of f(x) at £ = 1 is the Talor polynomial of degree 1 for f about z = 1. Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Result Correct Answer x-1 r—1 correct r—1 0.07 0.07 correct 0.07 All of the answers above are correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 19. (1 point) (k¥ ¥% %) The figure below shows f(x) and its linear approximation at = a, y = 4 — 5. (The linear approximation is shown in blue.) 1 8 (Click on the image to view an enlarged graph.) (@) What is the value of a? (b) What is the value of f(a)? = (c) Use the linear approximation to approximate the value of f(4.2). fa2)=| 18 (d) Is the approximation an under- or overestimate? The approximation is an { under v ]estimate. https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 11/15
05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 Solution: Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Result Correct Answer 4 4 correct 4 11 11 correct 11 11.8 11.8 correct 11.8 under under correct under All of the answers above are correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 20. (1 point) (k%% %) Let T3(z) be the Taylor Polynomial of degree three for f(x) centered at 0. If f(0) =71, f’(O) =14, f”(O) = —12, fm(o) =3 Ty(z) = [7+14x-6x"2-1/2x"3 Solution: preview answers Entered Answer Preview Result Correct Answer 1 1222 323 7+ 14%%-6*(xA2)-(1/2)*(x3) 7+ 14z — 622 — Em"' correct 7+ 14z — 2“’ _ % The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 21. (1 point) (% #%) At what value(s) of on the curve y = 1 4 250z3 — 32> does the tangent line have the largest positive slope? (If there is more than one value, enter your answer as a comma separated list.) Answer (separate by commas): z = -5, 5 preview answers Entered Answer Preview Correct Answer _5' g —5, 5 _5, 5 The answer above is correct. J https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 12/15
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05/12/23, 02.15 WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 22. (1 point) Note: If you are asked for value(s), give your answer as a single value (e.g. 17 ), or a comma separated list (e.g. 1,2,3 ), or NONE. If you are asked for an interval, give your answer in interval notation. Type INF for co and -INF for —o0. (¥ ¥ %) Consider the function f and its derivatives, all defined forz > 0 : f(z) = 2°log z, f'(z) = z* + 5z log z, " (z) = 92> + 2023 log z. a) Find the z-values of the critical points of f (you are not asked to enter them here) and then use the Second Derivative Test, when possible, to determine the location and types of the extrema. Local maxima atz = NONE (Separate multiple answers by commas, and enter NONE if there are no local maxima.) Local minima at z = e”?(-1/5) (Separate multiple answers by commas, and enter NONE if there are no local minima.) Solution: Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Result Correct Answer NONE NONE correct NONE 0.818731 e_Tl correct 0.818731 All of the answers above are correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 23. (1 point) (K> % %) Find two numbers differing by 38 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are -19, 19 . preview answers ] Entered Answer Preview Result Correct Answer -19, 19 —19,19 correct —-19,19 The answer above is correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 24. (1 point) https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 13/15
05/12/23, 02.15 (k%% %) For what positive value of k does the function y = sin(kt) satisfy the differential equation y"” + 81y = 07? : For what negative value of k does the function y = cos(kt) satisfy the differential equation y"” + 81y = 0? : WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 Note: You can earn partial credit on this problem. preview answers Entered Answer Preview Correct Answer 9 9 9 -9 -9 -9 All of the answers above are correct. J ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDEDJ Problem 25. (1 point) . . : logz+C . : : . . oy : (K3 %) Verify that every member of the family of functions y = ———— is a solution of the differential equation z“y" 4+ zy = 1. Answer the following T questions. 1. Find a solution of the differential equation that satisfies the initial condition y(9) = 10. Answer: Yy = { -89/81 2. Find a solution of the differential equation that satisfies the initial condition (10) = 9. Answer. Yy = [ 91/81 Note: You can earn partial credit on this problem. preview answers At least one of the answers above is NOT correct. Entered Answer Preview Result Correct Answer —89 , In(z) 4+ 87.8028 -1.09877 — incorrect 81 T 91 . In(z) + 87.6974 1.12346 8_1 incorrect = ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDED] Problem 26. (1 point) (K ¥ ¥ %) Use the symbols provided below to fill in the phase line for the differential equation z' = (z + 2)(z — 3). https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL 2023W1/quiz_mode/Practice_Quiz - unlimited_time,v1/ 14/15
05/12/23, 02.15 To place a symbol on the line: Click a symbol button, then click a point on the line. To remove a symbol from the line: Click the "delete” X button, then click the symbol on the line. decreasing increasing delete X steady state slope undefined < > o l WeBWorK : 2023W1 MATH 100A ALL 2023W1 : Practice Quiz - unlimited time : v1 preview answers Entered Answer Preview Result Correct Answer -<<-(dot at -2)-< <-(dot at 3)->>- -<<-(dot at -2)-<<-(dot at 3)->>- The answer above is NOT correct. incorrect 1,(2,-2),0, (2,3),1 ANSWERS ONLY CHECKED -- ANSWERS NOT RECORDED] Problem 27. (1 point) Once you're finished, hit submit to find your score. You must pass Part 1 of the final exam to pass the course. If you got fewer than 13 of the problems 2-26 correct, we strongly recommend that you revise and retry. Ok wv preview answers Entered Answer Preview Result Correct Answer Ok Ok correct The answer above is correct. Ok Jump to Problem: 1 % Score: 0 2 10 (0 100 900 900 50 100 900 900 900 400 100 900 (Q (0 89 4 Show correct answers Show Solutions [ Preview Test ][ Check Test ] Page generated at 12/05/2023 at 01:52am PST 17 18 19 20 WeBWorK © 1996-2022 | theme: math4 | ww_version: 2.17 | pg_version 2.17 | The WeBWorK Project https://webwork.elearning.ubc.ca/webwork2/2023W1_MATH_100A_ALL_2023W1/quiz_mode/Practice_Quiz_- unlimited_time,v1/ 21 22 23 24 25 26 27 100 100 100 40 (O Q0 100 < 15/15
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