math lecture notes3 [Notes & HW Answers] 5.1 How Do We Measure Distance Traveled? [Prepwork 5.1] Q1. Consider the velocity data for the car shown in table 5.1. Find lower and upper estimates for the distance it travels between 𝑡=4 and 𝑡=8. A: lower = 164 upper = 184 Write the difference between these as the following product: difference = (Δ𝑡)(Δ𝑣)= (2) (10) Q2. The velocity of a bicycle is given by v(t) = 4t feet per second, where t is the number of seconds after the bike sta.. 2022. 12. 6. [Notes & HW Answers] 4.3 Optimization and Modeling [Prepwork 4.3] Q1. Consider the following problem: You are standing on a river bank and want to get to a house that is on the other side of the river and 800 feet up the river as quickly as possible. The river is 100 feet wide. You can walk along the river at a speed of 5 ft/sec or swim across the river at a speed of 3 ft/sec. What path should you take? A: Which of the following quantities are y.. 2022. 12. 6. [Notes & HW Answers] 3.7 Implicit Functions [Prepwork 3.7] Q1. Which of the following points satisfies the equation 𝑥^2−𝑥𝑦^2=2? A: (1) (-2^(1/2)/2, (4.5)^(1/4)) ; (2) (-2^(1/2),0) Q2. (1) Find dy/dx when x^2 - xy^2 =2. A: (1) dy/dx = (y^2-2x)/-2xy (2) Find an equation for the tangent line to x^2 - xy^2 = 2 at the point (2,1). A: (2) y = (3/4)(x-2) + 1 Q3. Find all points satisfying the equation 𝑥2−𝑥𝑦2=2x2−xy2=2 where the tangent line is v.. 2022. 11. 21. 이전 1 다음
