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### Calc 2 Lab 5

Course: MATH 2020, Fall 2010
School: Ithaca College
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Ithaca College - MATH - 2020
Ithaca College - MATH - 2020
Ithaca College - MATH - 2020
Ithaca College - MATH - 2020
North Texas - MATH - 1400
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North Texas - MATH - 1400
Chapter 3Worksheet 3AName_ Period_Directions: On a separate sheet of graph paper sketch each function. Make sure you number and label each graph. Plot at least 2 points for accuracy. 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. y = x2 + 5 y = x+1+ 5 y = x3 +
North Texas - MATH - 1400
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North Texas - MATH - 1400
Chapter 3Worksheet 3DName_ Period_Directions: Determine whether each function below is even, odd, or neither. Explain. 1. y = 5x 1 0 - 3x 4 + 2 2. w = 10 x 9 - 2x 3 + x3.f(x ) = x4.g(x ) =1 xDirections: Determine which graphs below are even, odd
North Texas - MATH - 1400
Chapter 3Worksheet 3EName_ Period_Directions: Determine whether each function below is even, odd, or neither. Explain. 1 1. y= 2 2. f(x ) = -7x 4 + 6x - 3 x -13.4.5,6.Directions: For questions 7 and 8 the graphs below are portions of completed gra
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North Texas - MATH - 1400
WORKSHEET 1 1. Below is a list of some simple algebra problems. Some of the solutions are correct and some of them are wrong! For each problem: A. determine if the answer is correct; B. determine if there are any mistakes made in solving the problem and l
North Texas - MATH - 1400
WORKSHEET 2 - Fall 1995 1. For each graph below of a function f (x), sketch a graph of its derivative f (x): a) b) c)d)e)f)g)h)i)2. Without using the concept of a limit (and thus derivative), write the equations of all lines through the point (a, a
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WORKSHEET 4 - Fall 1995 1. The graph of f (x) is given below. Use it to graph the following: a) f (3x) e) f (x) + 1 b) f (x) f) 5f (x) c) f (2x) g) f (x + 2) d) f (x 1) h) 5f (3x + 2) + 1i) In your own words, describe the manner in which the graph of f (
North Texas - MATH - 1400
WORKSHEET 5 - Fall 19951. Use a calculator to ll in the table given and then make a guess at the given limit. x 3 a) lim = x3 x3x- 3 x-3 x 2 2.5 2.75 2.9 2.99 limitb) limx23x = 3x + 23x 3x + 2 x 1 1.5 1.75 1.9 1.99 limitc) lim1 = x0 x21 x2 x 1 0.
North Texas - MATH - 1400
WORKSHEET 6 - Fall 1995 1. A function is said to be continuous at a point x0 if i. f (x0 ) is dened; ii. lim f (x) exists;xx0iii. and lim f (x) = f (x0 ).xx0Determine whether the following functions are continuous at the points given. At discontinuous
North Texas - MATH - 1400
WORKSHEET 7 - Fall 1995 1. Let f (x) = x3 + 3x2 3x. a) At any point (x0 , y0 ) on the graph, what is the slope of the tangent line to the graph? b) The graph of f (x) has two tangent lines parallel to the line y = 6x + 100. Find the equations of these two
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WORKSHEET 9 - Fall 1995 1. Recall that sin2 (x) + cos2 (x) = 1. Write an expression for each trig function squared in terms of one of the other trig functions. a) sin2 (x) 2. Compute the limits. sin2 2x x0 x2 1 + cot2 3x d) lim x0 4x2 a) lim b) lim e) 1 c
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North Texas - MATH - 1400
WORKSHEET 12 - Fall 1995 1. Write f (x) as a composition of two functions in two dierent ways. Write f (x) as a composition of three functions. Dierentiate f (x). a) f (x) = x2 + 1 b) f (x) = sin x x x2 x+2 c) f (x) = (2x2 x)5/22. a) The radius of a bal
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WORKSHEET 19 - Fall 1995 1. In each of the following equations, suppose that each variable is actually a function of time t and dierentiate each expression with respect to t. a) x2 + y 2 = 100 s x+s = b) 5 1.5 c) 40y xy = 80 d) (x + 7)(7 gt2 ) = 9x, e) V
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WORKSHEET 22 - Fall 19951. The graph of the derivative of a function f (x) is given below.f2 1 3 4a) What are the critical points of f (x)? b) Which critical point(s) correspond to relative extrema? Are they maxima or minima? c) Can you determine any
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WORKSHEET 24 - Fall 19951.a) Find three distinct functions f (x) such that f (x) = 0 for all x. b) Find three distinct functions g (x) such that g (x) = 4x for all x. c) Find three distinct functions h(x) such that h (x) = 3x x2 for all x.2. Let f1 (x)
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WORKSHEET 25 - Fall 1995 In the theory of quantum mechanics, the Heisenberg uncertainty principle (also called the indeterminacy principle) states that experiment cannot simultaneously determine the exact value of a component of momentum, px say, of an ob
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WORKSHEET 26 - Fall 1995 1. What is area? a) List the geometric objects for which you know how to nd the area. Include the formula you would use (and, of course, the meaning of any variables used.) How do you know these formulas? b) Describe some geometri
North Texas - MATH - 1400
WORKSHEET 27 - Fall 1995 1. Below, the graph of f (x) = x2 is given. The line below the graph is the tangent line at x = 1. The lines above the graph connect the points (0, 0), (1, 1), and (2, 4).432112a) Find the area bounded by the tangent line,
North Texas - MATH - 1400
WORKSHEET 28 - Fall 1995 1. Consider the following denition: Denition. If f is a function dened on [a, b] and the sums i=1 f (ci )(xi xi1 ) approaches a certain number as the mesh of partitions of [a, b] shrinks toward 0 (no matter how the sampling number
North Texas - MATH - 1400
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North Texas - MATH - 1400
WORKSHEET 31- Fall 19951.a) Give the denition of a denite integral. b) State the Fundamental Theorem of Calculus. c) What is wrong with the following argument?2 1dt 1 = 2 t t2 11 1 = 2 13 1 = 1= 2 22)a) Let f (x) = 4x x2 . Draw a graph of this fu
North Texas - MATH - 1400
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North Texas - MATH - 1400
WORKSHEET - Fall 1995 1. Write down the denition of a denite integral. Take turns explaining the dierent parts to the members of your group. 2. Use the denition of the denite integral to compute the following integrals:5 1 n3x2 14x + 11n2 07x.Hint:
North Texas - MATH - 1400
WORKSHEET 34 - Fall 1995 1. Sketch the nite area whose boundary is composed of pieces of the curves x = 1 y 4 and x = y 2 1. a) Find the area of this region by integrating with respect to y . b) Find the area of this region by integrating with respect to
North Texas - MATH - 1400
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North Texas - MATH - 1400
WORKSHEET 36 - Fall 1995 1. Compute /2 /2sin(3x) cos(5x) dx.2. It is known that m parts (by weight) of chemical A combine with n parts of chemical B to produce a comound C. Suppose that the rate at which C is produced varies directly with the product o
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
North Texas - MATH - 1400
CALCULUS 1. Dierentiate: f (x) = log2 sin x 2. Dierentiate: f (x) = cos sin x 3. Dierentiate: f (x) = log4 10x 4. Dierentiate: f (x) = cos 5x 5. Dierentiate: f (x) = ln cos x 6. Dierentiate: f (x) = sin sin x 7. Dierentiate: f (x) = 32xTrancedental Func
North Texas - MATH - 1400
Answers:1. f (x) = (sin x)cos xx 1 x ln sin x + cos x sin x 2x2. f (x) = (cos x) 3. f (x) = xx[ln cos x + 1] ( sin x) 1 ln x + 24. f (x) = (ln x)log x5. f (x) = (cos x) 6. f (x) = 7. f (x) = x xx1 1 log x ln ln x + (ln 10)x x ln x 1 x ln cos
North Texas - MATH - 1400
CALCULUSTrancedental Functions. Higher Derivatives1. Find f (x), f (x), f (x), and f (4) (x) for the following function: f (x) = 2 sin(3x) 2. Find f (x), f (x), f (x), and f (4) (x) for the following function: f (x) = 5 log(5x) 3. Find f (x), f (x), f (
North Texas - MATH - 1400
CALCULUSTrancedental Functions. Velocity and Acceleration1. Find the velocity, acceleration, and jerk functions for the following position function: s(t) = 3 log(t) 2. Find the velocity, acceleration, and jerk functions for the following position functi