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MATH 11510

[Notes & HW Answers] 5.2 The Definite Integral [Prepwork 5.2] Q1. Following example 1 in the text, suppose we considered n=4 to approximate the integral. What are each of the following? A: Δt= 0.25; f(t2)= 1/1.5 Q2. Find the exact value of the following integral. A: ∫^2_(-2) (4-x^2)^(1/2) dx = 2π Estimate the total area between f(x)=cos⁡(x4) and the x-axis for (0≤x≤π)^(1/4)(Note: you will want to sketch the curve y=f(x). Shade the regions be.. 2022. 12. 6.
[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] 3.10 Theorems About Differentiable Functions 2022. 11. 29.
[Notes & HW Answers] 3.9 Linear Approximation [Prepwork 3.9] Q1. What is the value at x=.1 of the local linearization L(x) of (1+x)^5 at x=0? A: L(0.1) = 1.5 Q2. Suppose you use the tangent line approximation near t=4 to estimate s′(4.05), where s(t) is a function that is always concave up. Then your answer is an A: underestimate Q3. Suppose the linear approximation of g(x)g(x) near x=6 is given by L(x)=5(x−6)−12. A:Then g(6) = -12 and g'(6.. 2022. 11. 21.
[Notes & HW Answers] 3.6 The Chain Rule and Inverse Functions [Prepwork 3.6] Q1. Let 𝑔(𝑥)g(x) be an invertible, differentiable function with values given in the table below. 𝑥 2 5 8 𝑔(𝑥) 8 2 0 𝑔′(𝑥) -2 -0.25 -0.1 Find a formula for the tangent line of 𝑔^(−1)(𝑥) at 𝑥=2. A: y = -4(x-2)+5 Q2. Find the derivative of 𝑓(𝑥)=arctan(5ln(𝑥)). A: f'(x) = 5/(x*(25*ln^2(x)+1) [HW 3.6] Q1. Find the derivative of the function f(t), below. f(t) = ln(t^9 +8) A: f'(t) = 9t^.. 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.
[WeBWork] Prepwork & HW 2.1~2.6 & 3.10 Answers Keywords: derivative, speed, acceleration, instantaneous velocity, changing, derivative function, the second derivative, differentiability Questions Example: [Prepwork 2.4] Q2. The cost of extracting T tons of ore from a copper mine is C = f (T) dollars. What does it mean to say that f 0(3400) = 250? A. When 3400 tons of ore have already been extracted from the mine, the cost of extracting the n.. 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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