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Calculus20

[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] 3.3 The Product and Quotient Rules [Prepwork 3.3] Q1. Which of the following are possible formulas for a function y = f (x) such that f'(x) = 10x^9*e^x+x^10*e^x? • A. x10ex+10 • B. 3+x10ex • C. x10ex+1 • D. 9x9ex−1 • E. x10ex+10 • F. 10x10ex • G. x10ex A: ABG Q2. Which (single) rule would one use to differentiate f (x) =x*e^x? A: the Product rule [HW 3.3] Q1. Find the derivative of the function f (x), below. It may be to your adv.. 2022. 10. 30.
[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.
[Notes & HW Answers] 3.1 Powers and Polynomials [Prepwork 3.1] Q1. For the derivative of 6x^6+4x^5+1x^4, what is the value of the coefficient of x^5? A: the coefficient is 36. Q2. Find the slope of the tangent line to f (x) = x^3 +x^2 +6/x at the point where x = 1. A: -1. [HW 3.1] Q1. Find the derivative of h(q) = 1/(q)^(1/4) . A: h'(q) = (-1/4)*(1/(q)^(4/5) Q2. Find the derivative of y = 10t^5−8t^(1/2) + 9/t. A: dy/dt = 50t^4-4t^(-1/2)-9t^(-.. 2022. 10. 28.
[Notes] Ch.2 Key Concept: The Derivative Keywords: derivative, speed, acceleration, instantaneous velocity, changing, derivative function, the second derivative, differentiability Preview the notes: Keywords: derivative, speed, acceleration, instantaneous velocity, changing, derivative function, the second derivative, differentiability 2022. 10. 28.
[WeBWork] Prepwork 1.3-1.8 & HW 1.1-1.8 Keywords: Keywords: functions, exponential functions, function transitions, logarithmic functions, trigonometric functions, powers, polynomials, rational functions, limits and continuity. Preview the files: 2022. 10. 13.
[Notes] Ch.1 Foundation for calculus_Functions & Limits Math 115 Textbook: Deborah Hughes-Hallett - Calculus Single Variable (2017, Wiley) - libgen.lc Preview the notes: Keywords: functions, exponential functions, function transitions, logarithmic functions, trigonometric functions, powers, polynomials, rational functions, limits and continuity. 2022. 10. 13.

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