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calculus lecture notes8

[Notes & HW Answers] 6.2 Constructing Antiderivatives Analytically [Prepwork 6.2] Q1. If 𝐹(𝑥) is an antiderivative of 𝑓(𝑥), what is the most general antiderivative? A: The most general antiderivative = F(x) + C Q2. Using the properties of antiderivatives in theorem 6.1 to find ∫(3cos(𝑥)+2sin(𝑥))𝑑𝑥 A: ∫(3cos(𝑥)+2sin(𝑥))𝑑𝑥= 3sin(x) - 2cos(x) + C Q3. Use the Fundamental Theorem to calculate the following integral exactly: A: ∫^(𝜋/3)_0 (2/cos^2𝜃) 𝑑𝜃= 2tan(𝜋/3) - 2t.. 2022. 12. 8.
[Notes & HW Answers] 6.1 Antiderivatives Graphically and Numerically [Prepwork 6.1] Q1. Enter two different antiderivatives of 𝑓=2𝑥. A: Antiderivative 1 = x^2+1 Antiderivative 2 = x^2+2 Q2. Suppose that the graph of 𝑓′f′ is given below. At what 𝑥 value does 𝑓 cease being linear? 𝑥= 1 At what 𝑥 value does the maximum value of 𝑓 occur? 𝑥= 3 Q3. Suppose that 𝐹′(𝑡)=𝑡cos(𝑡) and 𝐹(0)=3. Use the data and method from example 5 in the text to estimate each of the followin.. 2022. 12. 8.
[Notes & HW Answers] 5.4 Theorems about Definite Integral [Prepwork 5.4] Q1. For some function f, suppose that for some a∫^b_a f(x) dx=7 and ∫^c_a f(x) dx=9. Find each of the following. A: ∫^a_b f(x) dx= −7 ;∫^c_b f(x) dx= 2 Q2. Use the technique of example 2 in the text to evaluate the integral ∫^2_(−2) (|2x|+3) dx exactly. A: ∫^2_−2 (|2x|+3) dx = 20 Q3. Using a calculator to evaluate the appropriate integral, find the average value of P = f(t) = 2.03.. 2022. 12. 6.
[Notes & HW Answers] 5.3 The Fundamental Theorem of Calculus [Prepwork 5.3] Q1. Around the beginning of the 1800’s, the population of the U.S. was growing at a rate of about 1.37t million people per decade, with t being measured in decades from 1810.If the population P(t) was 7.2 million people in 1810, estimate the population in 1820 (one decade later) by considering the work in example 2. A: P(1)= 8.375309 Q2. Given the CO2 addition rate shown in exampl.. 2022. 12. 6.
[Notes & HW Answers] 4.6 Related Rates [Prepwork 4.6] Q1. In example 4, how fast is the fuel consumption changing if instead the car is moving 30 mph and decelerating at a rate of 3000 miles/hr^2? Answer: Decreasing at a rate of approximately (choose the closest answer) 600 mpg/hr. Q2. A spherical snowball is melting. Its radius decreases at a constant rate of 3 cm per minute from an initial value of 100 cm. How fast is the volume de.. 2022. 12. 6.
[Notes & HW Answers] 4.5 Applications to Marginality [Prepwork 4.5] Q1. What is the relationship between (total) cost and marginal cost? A: Marginal cost is the derivative of total cost Q2. Suppose C and R are the cost and revenue functions for a particular product. Check all the statements below that are true. A. The critical points of the profit function happen when 𝑀𝑅=𝑀𝐶 or one of these derivatives does not exist. B. The profit is maximized whe.. 2022. 12. 6.
[Notes & HW Answers] 4.4 Families of Functions and Modeling 2022. 12. 6.
[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.

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