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Calculus 1 Summary Notes [Chapter 1. FOUNDATION FOR CALCULUS: FUNCTIONS & LIMITS] 1.1 Functions and Change 1.2 Exponential Functions 1.3 New Functions from Old 1.4 Logarithmic Functions 1.5 Trigonometric Functions 1.6 Powers, Polynomials, and Rational Functions 1.7 Introduction to Limits and Continuity 1.8 Extending the Idea of a Limit [Chapter 2. KEY CONCEPT: THE DERIVATIVE] 2.1 How Do We Measure Speed? 2.2 The Derivat.. 2022. 12. 13.
[Notes & HW Answers] 4.4 Families of Functions and Modeling 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] 4.2 Optimization [Prepwork 4.2] Q1. Which of the following examples satisfy the hypotheses of the Extreme Value Theorem on the given interval? (A) k(x)={3x^2+9 for 0≤xf(x)=2x^3−12x^2+18x+16. Find the minimal value of f(x) on the interval −1≤x≤2. Answer: The minimum value of f(x) on this interval is −16 and occurs at x=−1. Q3. Suppose f(x)f(x) is a continuous function defined on −∞𝑔(𝑡)=6𝑡𝑒^(−5𝑡) if 𝑡>0. A: global.. 2022. 12. 6.
[Notes & HW Answers] 4.1 Using First and Second Derivatives [Prepwork 4.1] Q1. Suppose f(x)f(x) is a continuous function that has a local maximum at the point (3,2).Which of the following statements must be true? A: (1) If a is just a little greater than 3, then f(a) ≤ 2. (2) f(x) has a critical point at x=3. (3) If a is just a little less than 3, then f(a) ≤ 2. Q2. Suppose f(x)f(x) is a continuous function that has a local minimum at (1,6)(1,6) and no o.. 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.
[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.
[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.

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