Precalculus (10th Edition)
10th Edition
ISBN: 9780321979070
Author: Michael Sullivan
Publisher: PEARSON
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Chapter B.2, Problem 28E
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MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
Chapter B Solutions
Precalculus (10th Edition)
Ch. B.1 - In Problems determine the coordinates of the...Ch. B.1 - In Problems determine the coordinates of the...Ch. B.1 - In Problems determine the coordinates of the...Ch. B.1 - In Problems determine the coordinates of the...Ch. B.1 - In Problems 510, determine the viewing window...Ch. B.1 - In Problems 510, determine the viewing window...Ch. B.1 - In Problems 510, determine the viewing window...Ch. B.1 - In Problems 510, determine the viewing window...Ch. B.1 - In Problems determine the viewing window...Ch. B.1 - In Problems 1116, select a setting so that each of...
Ch. B.1 - In Problems select a setting so that each of the...Ch. B.1 - In Problems select a setting so that each of the...Ch. B.1 - In Problems select a setting so that each of the...Ch. B.1 - In Problems 1116, select a setting so that each of...Ch. B.1 - In Problems 1116, select a setting so that each of...Ch. B.1 - In Problems select a setting so that each of the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - In Problems graph each equation using the...Ch. B.2 - In Problems 116, graph each equation using the...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - For each of the above equations, create a table,...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - 1732. For each of the above equations, create a...Ch. B.2 - For each of the above equations, create a table,...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems 16, use Zero (or ROOT) to approximate...Ch. B.3 - In Problems 16, use Zero (or ROOT) to approximate...Ch. B.3 - In Problems 16, use Zero (or ROOT) to approximate...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems 712, use Zero (or ROOT) to approximate...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems 712, use Zero (or ROOT) to approximate...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems use Zero (or ROOT) to approximate the...Ch. B.3 - In Problems 712, use Zero (or ROOT) to approximate...Ch. B.5 - Prob. 1ECh. B.5 - Prob. 2ECh. B.5 - Prob. 3ECh. B.5 - Prob. 4ECh. B.5 - Prob. 5ECh. B.5 - Prob. 6ECh. B.5 - Prob. 7ECh. B.5 - Prob. 8ECh. B.5 - If Xmin=4,Xmax=12, and Xscl=1, how should...Ch. B.5 - If and how should and be selected so that the...
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- 3. Use the graph for problem #35, p175 to answer the questions. The average price (in cents) per gallon of unleaded gasoline in the United States for the years 2010 to 2019 is shown in this chart. Find the average rate of change per year in the average price per gallon for each time period. Source: U.S. Energy Information Administration. a) 2010 to 2013 b) 2012 to 2018 c) 2014 to 2019arrow_forward4. Researchers at Iowa State University and the University of Arkansas have developed a piecewise function that can be used to estimate the body weight (in grams) of a male broiler during the first 56 days of life according to W(t)=48+3.64t+0.6363²+0.00963 t³ if 1St≤28, -1004+65.8t if 28arrow_forward3. Given the function h(x)=(x²+x-12 if x≤1 3-x if x>1' a) Graph the function h(x). Make the graph big enough to be easily read using the space below. Be sure to label all important aspects of the graph. b) Find all values of x where the function is discontinuous. c) Find the limit from the left and from the right at any values of x found in part b.arrow_forward2. Find the instantaneous rate of change for each function f(x)=2x²-x+3 at x=0..arrow_forward4x-3 2. Determine the interval over which the function is continuous. x+4arrow_forward1. Find the average rate of change for the following functions over the given intervals. a) f(x)=4x-2x²+3x between x=-1 and x=4 b) y lnx between x=1 and x=4arrow_forward1. Find all values x=a where the function is discontinuous, determine if the discontinuity is removable or non- removable. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist and explain how you know. a) f(x)= 2-x x²(x+5) b) f(x)= x²-9x x²+3x c) p(x)=-3x²+2x²+5x-8arrow_forwardDo the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.arrow_forward12. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.508.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x + 16 dx X Need Help? Read It SUBMIT ANSWER 13. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.512.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx 8)(2x + 1) Need Help? Read It SUBMIT ANSWER 14. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.518.XP. Find the area of the region under the given curve from 1 to 5. y = x² +7 6x - x² Need Help? Read It ASK YOUR TEAarrow_forwardDETAILS MY NOTES SESSCALCET2 6.3.012. 6. [-/1 Points] Evaluate the integral. x-4 dx x² - 5x + 6 Need Help? Read It SUBMIT ANSWER 7. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.019. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x²+1 (x-6)(x-5)² dx Need Help? Read It SUBMIT ANSWER 8. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.021. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ✓ x² 4 +4 dxarrow_forwardDETAILS MY NOTES SESSCALCET2 6.3.017. 1. [-/1 Points] Evaluate the integral. - - dy y(y + 2)(y-3) Need Help? Read It Watch It SUBMIT ANSWER 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.027. Evaluate the integral. (Use C for the constant of integration.) X + 16 x²+10x29 dx Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardDo the Laplace Transformation for this equation in Partial Fractions.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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