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study help
mathematics
precalculus
Questions and Answers of
Precalculus
Express the sums in sigma notation. The form of your answer will depend on your choice of the lower limit of summation.1 + 2 + 3 + 4 + 5 + 6
Express the sums in sigma notation. The form of your answer will depend on your choice of the lower limit of summation. 1 + 2|5 T + -
Express the sums in sigma notation. The form of your answer will depend on your choice of the lower limit of summation.1 + 4 + 9 + 16
Oil is leaking out of a tanker damaged at sea. The damage to the tanker is worsening as evidenced by the increased leakage each hour, recorded in the following table.a. Give an upper and a lower
A power plant generates electricity by burning oil. Pollutants produced as a result of the burning process are removed by scrubbers in the smokestacks. Over time, the scrubbers become less efficient
An object is shot straight upward from sea level with an initial velocity of 400 ft / sec. a. Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity
Express the sums in sigma notation. The form of your answer will depend on your choice of the lower limit of summation.2 + 4 + 6 + 8 + 10
Use a finite sum to estimate the average value of ƒ on the given interval by partitioning the interval into four subintervals of equal length and evaluating ƒ at the subinterval midpoints.ƒ(x) =
Use a finite sum to estimate the average value of ƒ on the given interval by partitioning the interval into four subintervals of equal length and evaluating ƒ at the subinterval midpoints.ƒ(x) =
Inscribe a regular n-sided polygon inside a circle of radius 1 and compute the area of the polygon for the following values of n:a. 4 (square) b. 8 (octagon) c. 16d. Compare the areas in
Graph each function ƒ(x) over the given interval. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum Σ4k =1ƒ(ck)
Graph each function ƒ(x) over the given interval. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum Σ4k =1ƒ(ck)
Graph each function ƒ(x) over the given interval. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum Σ4k =1ƒ(ck)
Graph each function ƒ(x) over the given interval. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum Σ4k =1ƒ(ck)
Find the norm of the partition P = {0, 1.2, 1.5, 2.3, 2.6, 3}.
Find the norm of the partition P = {-2, -1.6, -0.5, 0, 0.8, 1}.
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as n→ ∞ to
Find f′(x) and f′(c). Function f(x) = (2x²-3x) (9x + 4) Value of c c = -1
Find f′(x) and f′(c). Function f(x) x - 4 x + 4 Value of c c=3
Find f′(x) and f′(c). Function sin x X Value of c C T 6
Find the indefinite integral and check the result by differentiation. Ja. (1 + 6x)4(6) dx
Find the indefinite integral and check the result by differentiation. √6²-5 (x² - 9)³(2x) dx
Find the indefinite integral and check the result by differentiation. √ √/25 - x² (-2x) dx
Explain how to use the Constant Multiple Rule when finding an indefinite integral.
In your own words, summarize the guidelines for making a change of variables when finding an indefinite integral.
Explain how to find the area of a plane region using limits.
Find the indefinite integral and check the result by differentiation. 3/3 4x²(-8x) dx
Find the particular solution of the differential equation that satisfies the initial condition(s).f'(x) = -6x, f (1) = -2
Find the indefinite integral and check the result by differentiation. x³(x4 + 3)² dx
Find the indefinite integral and check the result by differentiation. [x²(6 - x³)³ dx
Find the particular solution of the differential equation that satisfies the initial condition(s).f'(x) = 9x2 +1, f (0) = 7
A ball is thrown vertically upward from ground level with an initial velocity of 96 feet per second. Assume the acceleration of the ball is a(t) = -32 feet per second per second. (Neglect air
Find the indefinite integral and check the result by differentiation. [1² (21³. x²(2x³ - 1)4 dx
Find the indefinite integral and check the result by differentiation. x(5x² + 4)³ dx
Find the indefinite integral and check the result by differentiation. t√1² + 2 dt
With what initial velocity must an object be thrown upward (from a height of 3 meters) to reach a maximum height of 150 meters? Assume the acceleration of the object is a(t) = 9.8 meters per second
Find the indefinite integral and check the result by differentiation. SPVZH 13√√214 + 3 dt
Find the indefinite integral and check the result by differentiation. 5x 3/1 - x² dx
Find the indefinite integral and check the result by differentiation. I 6uu + 8 du 7
Find the indefinite integral and check the result by differentiation. 7x (1-x²)3 dx
Find the indefinite integral and check the result by differentiation. x3 (1 + x)² xp.
Find the indefinite integral and check the result by differentiation. x² (1 + x³)2 dx
Find the indefinite integral and check the result by differentiation. 6x² (4x³ - 9)3 dx
Find the indefinite integral and check the result by differentiation. x 1-x² dx
Find the indefinite integral and check the result by differentiation. [ ( ₁ + ² ) ( 1 ) di dt
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function f(x) = 4x
Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width.)y = 10/ x2 + 1 10 8 6 4 2 y 1 2 -X
Find the indefinite integral and check the result by differentiation. x³ 3 1 + x4 ¡dx
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function f(x) =
Find the indefinite integral and check the result by differentiation. [ (8 - 11) ² ( 1 ) di dt
Find the indefinite integral and check the result by differentiation. 20 dx
Find the indefinite integral and check the result by differentiation. X 3/5x2 dx
Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region.y = 5 - x2, [-2, 1]
Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region.y = 1/4 x3, [2, 4]
Find the general solution of the differential equation.dy/dx = 10x2/ √1 + x3
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval.f (x) = 16 - x2, [0, 4]
Find the general solution of the differential equation.dy/dx = x + 1/(x2 + 2x - 3)2
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval.f (x) = sin πx, [0, 1]
Find the general solution of the differential equation.dy/dx = 18 - 6x2 /√x3 - 9x + 7
Evaluate the definite integral by the limit definition.∫5-3 6x dx
Evaluate the definite integral by the limit definition.∫30 (1- 2x2) dx
Sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral.∫6-6 √36 - x2 dx
Find the indefinite integral.∫ π sin πx dx
Find the indefinite integral.∫ sin 4x dx
Use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result.∫60 (x - 1) dx
Find the indefinite integral.∫ cos 6x dx
Use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result.∫1-2 (4x4 - x) dx
Find the indefinite integral.∫ csc2 (x/2) dx
Find the indefinite integral.∫ 1/θ2 cos 1/θ dθ
Find the indefinite integral.∫ x sin x2 dx
Find the indefinite integral.∫ sin 2x cos 2x dx
Use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result.∫π/4-π/4 sec2 t dt
Find the area of the given region.y = sin x y 14 2 3 +1° X
Find the area of the given region.y = x + cos x -회 3 2 y 2 tenta X
Find the indefinite integral.∫ 3 √tan x sec2 x dx
Find the indefinite integral.∫ csc2 x /cot3 x dx
Find the indefinite integral.∫ sin x / cos3 x dx
Find the area of the region bounded by the graphs of the equation.y = √x(1- x), y = 0
Find the indefinite integral by making a change of variables.∫ x2 √1- x dx
Find the indefinite integral by making a change of variables.∫ x√x + 6 dx
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.f (x) = 3x2, [1, 3]
Find the indefinite integral by making a change of variables.∫ x √3x - 4 dx
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.f (x) = sin x, [0, π]
Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value.f (x) = 1/√x, [4, 9]
Find the indefinite integral by making a change of variables.∫ (x + 1) √2 - x dx
Find the indefinite integral by making a change of variables.∫ x2 - 1 / √2x - 1 dx
Evaluate the definite integral. Use a graphing utility to verify your result. 2x²√√x³ + 1 3+1 dx dx
Evaluate the definite integral. Use a graphing utility to verify your result. x³(2x4 + 1)² dx
Evaluate the definite integral. Use a graphing utility to verify your result. J -1 x√1-x² dx
Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value.f (x) = x3, [0, 2]
Use the Second Fundamental Theorem of Calculus to find F'(x).F(x) = ∫x1 1/t2 dt
Find the indefinite integral by making a change of variables.∫ cos3 2x sin 2x dx
Find the indefinite integral.∫ x(1 - 3x2)4 dx
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