derivatives3 [Notes & HW Answers] 3.5 The Trigonometric Functions [Prepwork 3.5] Q1. The Bay of Monterey in California is known for extreme tides. The depth of the water, y, in meters can be modeled as a function of time, t, in half-hours after midnight, by y=12+6cos(t). How quickly is the depth of the water rising or falling at 3 a.m.? (Make sure you compute this in radians and give your answers to three decimal places.) Rising at (in m/half-hours) A: 1.676 Q.. 2022. 11. 21. [Notes & HW Answers] 3.4 The Chain Rule [Prepwork 3.4] Q1. The length,L, in micrometers (𝜇μm), of steel depends on the air temperature degrees celsius, and the temperature depends on time,t, measured in hours. If the length of a steel bridge increases by 0.25μm for every degree increase in temperature, and the temperature is increasing at 4 degrees celsius per hour, how fast is the length of the bridge increasing? A: At a rate of 1 μm.. 2022. 11. 21. [Notes & HW Answers] 3.2 The Exponential Functions [Prepwork 3.2] Q1. Let f (x) = x^10 +10^x. Find the first and second derivatives of f(x). A: f'(x) = 10x^9 + (ln 10)10^x ; f''(x) = 90x^8+(ln 10)(ln10)10^x Q2. For what value of a is y = 1+5x the tangent line for y = ax at x = 0? A: a = e^5 [HW 3.2] Q1. Find the derivative of y = 4x^8+8^x+12. A: dy/dx = 32x^7 + (ln 8)8^x Q2. Find the derivative of z = (ln 10)e^x. A: dz/dx = (ln 10)e^x. Q3. Find .. 2022. 10. 28. 이전 1 다음
