test3p - centimeters per second. i. Write a formula for...

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Practice Midterm #3 1. Trig Functions (a) Find the derivatives of the following functions. i. y = sec x ii. T = 5 - t cos(4 πt ) (b) If a 10 inch pendulum is swinging so that the angle θ of the pendulum with the vertical axis is given by θ = . 25 cos(8 πt ), where t is the time in seconds, what is the rate of change of θ when t = 3? (c) Verify y = cos 2 x + sin 2 x satisfies the equation y 00 + 4 y = 0.
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2. Chain Rule (a) State the General Power Rule. (b) Find the derivatives of the following functions. i. f ( x ) = (2 x - 7) 3 ii. h ( t ) = t 3 t - 4
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3. Higher-Order Derivatives and Implicit Differentia- tion (a) If the position of a car is given by p = 5 t 2 + 20 t feet (t is in seconds), what is the car’s acceleration? (b) Find dy/dx for the following equations. i. x 2 y 2 - 4 y = 1 ii. tan( x + y ) = x
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4. Related Rates (a) If xy = 4, find dy/dt given that x = 8 and dx/dt = 16. (b) Consider a cube whose edges are expanding at a rate of 3
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Unformatted text preview: centimeters per second. i. Write a formula for volume V in terms of edge length l , and for surface area S in terms of edge length l . ii. Find a formula for how fast the surface area is changing over time. iii. How fast is the volume changing when the edges have length 2? 5. True/False Mark each question as ( T )rue or ( F )alse. a. The volume of a sphere of radius r is 4 r 3 / 3. b. An expression for dy/dx cannot contain any occurrences of y . c. If f ( x ) is an n th degree polynomial, then f (5) ( x ) = 0. d. Acceleration is the second derivative of position. e. The Chain Rule states that d dx [ f ( g ( x ))] = f ( x ) g ( x ). f. The derivative of csc x is-csc x cot x ....
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test3p - centimeters per second. i. Write a formula for...

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