Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-4π/6)
> Differentiate (with respect to t or x): y = sin 2x cos 3x
> Differentiate (with respect to t or x): y = (cos x + sin x)2
> Differentiate (with respect to t or x): y = ex sin x
> Differentiate (with respect to t or x): y = cos2 x + sin2 x
> Differentiate (with respect to t or x): y = cos2 x3
> Differentiate (with respect to t or x): y = 3√(sin π t)
> The volume (V) of a certain amount of a gas is determined by the temperature (T) and the pressure (P) by the formula V = .08(T/P). Calculate and interpret ∂V/∂P and ∂V/∂T when P = 20, T = 300.
> Differentiate (with respect to t or x): y = (1 + cos t)8
> Differentiate (with respect to t or x): y = ecos x
> Differentiate (with respect to t or x): y = √ sin(x - 1)
> Differentiate (with respect to t or x): y = cos(ex)
> Differentiate (with respect to t or x): y = sin √(x – 1)
> Differentiate (with respect to t or x): y = sin3 t2
> Differentiate (with respect to t or x): y = cos3 t
> Differentiate (with respect to t or x): y = cos (2x + 2) / 2
> Differentiate (with respect to t or x): y = sin (π - t)
> Differentiate (with respect to t or x): y = t cos t
> The demand for a certain gas-guzzling car is given by f (p1, p2), where p1 is the price of the car and p2 is the price of gasoline. Explain why ∂f/∂p1 < 0 and ∂f/∂p2 > 0.
> Let g (x, y, z) = x/(y - z). Compute g (2, 3, 4) and g (7, 46, 44).
> Differentiate (with respect to t or x): y = t cos t
> Differentiate (with respect to t or x): y = - sin 3t / 3
> Differentiate (with respect to t or x): y = 2 cos 3t
> Differentiate (with respect to t or x): y = cos (- 4t)
> Differentiate (with respect to t or x): y = 4 sin t
> Differentiate (with respect to t or x): y = 2 cos 2t
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 16 4 1
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 3 2
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t √5 2
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 2 t √3 1
> Let p1 be the average price of MP3 players, p2 the average price of audio files, f (p1, p2) the demand for MP3 players, and g (p1, p2) the demand for audio files. Explain why ∂f/∂p2 < 0 and ∂g/∂p1 < 0.
> In any given locality, the length of daylight varies during the year. In Des Moines, Iowa, the number of minutes of daylight in a day t days after the beginning of a year is given approximately by the formula (Source: School Science and Mathematics.) (
> In any given locality, tap water temperature varies during the year. In Dallas, Texas, the tap water temperature (in degrees Fahrenheit) t days after the beginning of a year is given approximately by the formula (Source: Solar Energy.) (a) Graph the fu
> Assume that sin(.42) = .41. Use properties of the cosine and sine to determine sin(-.42), sin(6p - .42), and cos(.42).
> Assume that cos(.19) = .98. Use πroπerties of the cosine and sine to determine sin(.19), cos(.19 - 4π), cos(-.19), and sin(-.19).
> Determine the value of cos t when t = 5π, -2π, 17π>2, -13π>2.
> Determine the value of sin t when t = 5π, -2π, 17π>2, -13π>2.
> Use the unit circle to describe what happens to sin t as t increases from π to 2π.
> Refer to Fig. 10. Describe what happens to cos t as t increases from 0 to Ï€. Figure 10: (a) P T I (d) P Ø (b) P (e) P O
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -cos t
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = cos t
> Refer to Exercise 27. Let g (p1, p2) be the number of people who will take the train when p1 is the price of the bus ride and p2 is the price of the train ride. Would you expect ∂g/∂p1 to be positive or negative? How about ∂g/∂p2? Exercise 27: In a cert
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(-π>3)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(π>6)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = -sin(3π>8)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(-4π>3)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(7π>6)
> Find t such that -π>2 ≤ t ≤ π>2 and t satisfies the stated condition. sin t = sin(3π>4)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-3π/4)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-5π/8)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(5π/4)
> In a certain suburban community, commuters have the choice of getting into the city by bus or train. The demand for these modes of transportation varies with their cost. Let f (p1, p2) be the number of people who will take the bus when p1 is the price of
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(3π/2)
> Find t such that 0 ≤ t ≤ π and t satisfies the stated condition. cos t = cos(-π>/6)
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and b = 3.5, find a and c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .5 and a = 2.4, find b and c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .9 and c = 20.0, find a and b. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .4 and a = 10.0, find c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = .4 and c = 5.0, find a. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and b = 3.2, find c. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. If t = 1.1 and c = 10.0, find b. Figure 16: t a b
> Refer to various right triangles whose sides and angles are labeled as in Fig. 16. Round off all lengths of sides to one decimal place. Estimate t if a = 12, b = 5, and c = 13. Figure 16: t a b
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: 2 2= ex² + e-4y² 2 e (b) 2₂x0 몸 라 (d) 2.
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t (.8, -.6)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-.6, -.8)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (.6, .8)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-2, 2)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (2, -3)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. (-2, 1)
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. t 3 5
> Give the values of sin t and cos t, where t is the radian measure of the angle shown. 13, t 12
> Convert the following to radian measure. 990˚ , - 270˚ , - 540˚
> Convert the following to radian measure. 450˚ , -210˚ , -90˚
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: NY 2 15x²y²e-2². x² + y² 150 107 e (b) 2₂x0 몸 라 (d) 2.
> Convert the following to radian measure. 18 ˚, 72˚ , 150 ˚
> Convert the following to radian measure. 30 ˚, 120˚, 315˚
> Construct angles with the following radian measure. 2π/3, - π/6, 7π/2
> Construct angles with the following radian measure. π/6, - 2π/3, - π
> Construct angles with the following radian measure. - π/4, - 3π/2, - 3π
> Construct angles with the following radian measure. - π/3, - 3π/4, - 7π/2
> Construct angles with the following radian measure. π/3, 5π/2, 6π
> Construct angles with the following radian measure. 3π/2, 3π/4, 5π
> Give the radian measure of each angle described.
> Give the radian measure of each angle described. 0
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: x 2 z = x² - x² - y² 2 e (b) 2₂x0 몸 라 (d) 2.
> Give the radian measure of each angle described.
> Give the radian measure of each angle described.
> Give the radian measure of each angle described.
> Give the radian measure of each angle described.
> Give the radian measure of each angle described.
> Give the radian measure of each angle described.
> Let f (x, y, λ) = xy + λ (5 - x - y). Find f (1, 2, 3).
> If A dollars are deposited in a bank at a 6% continuous interest rate, the amount in the account after t years is f (A, t) = Ae0.06t. Find and interpret f (10, 11.5).
> Let f (x, y, z) = x2ey/z. Compute f (-1, 0, 1), f (1, 3, 3), and f (5, -2, 2).
> Let f (x, y) = x√y/(1 + x). Compute f (2, 9), f (5, 1), and f (0, 0).
> Match the graph of the function to the systems of level curves shown in Figs. 8(a)–(d). Figure 8: 2 -4 1 + x² + 2y² 2 e (b) 2₂x0 몸 라 (d) 2.
> The present value of y dollars after x years at 15% continuous interest is f (x, y) = ye-0.15x. Sketch some sample level curves. (Economists call this collection of level curves a discount system.)
> Let R be the rectangle consisting of all points (x, y), such that 0 ≤ x ≤ 4, 1 ≤ y ≤ 3, and calculate the double integral. ∫R∫ 5 dx dy
> Let R be the rectangle consisting of all points (x, y), such that 0 ≤ x ≤ 4, 1 ≤ y ≤ 3, and calculate the double integral. ∫R∫ (2x + 3y) dx dy
> Calculate the iterated integral. ∫05 (∫14 (2xy4 + 3) dy) dx
> Calculate the iterated integral. ∫01 (∫04 (x√y + y) dy) dx
