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study help
mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
Find parametric equations for the line that is tangent to the curve of intersection of the surfaces at the given point. Surfaces: Point: x² + 2y + 2z = 4, y = 1 (1, 1, 1/2)
Find equations for the lines that are tangent and normal to the level curve ƒ(x, y) = c at the point P0. Then sketch the lines and level curve together with ∇ƒ at P0. y - sin x sin x 1, = Po(π, 1)
Find parametric equations for the line that is tangent to the curve of intersection of the surfaces at the given point. Surfaces: Point: x + y² + z = 2, y = 1 (1/2, 1, 1/2)
Sketch the surface ƒ(x, y, z) = c together with ∇ƒ at the given points.y2 + z2 = 4; (2, ±2, 0), (2, 0, ±2)
Find an equation for the plane tangent to the level surface ƒ(x, y, z) = c at the point P0. Also, find parametric equations for the line that is normal to the surface at P0.x2 - y - 5z = 0, P0(2, -1, 1)
Find an equation for the plane tangent to the level surface ƒ(x, y, z) = c at the point P0. Also, find parametric equations for the line that is normal to the surface at P0.x2 + y2 + z = 4, P0(1, 1, 2)
Verify that wxy = wyx.w = xy2 + x2y3 + x3y4
Verify that wxy = wyx.w = x sin y + y sin x + xy
You plan to calculate the volume inside a stretch of pipeline that is about 36 in. in diameter and 1 mile long. With which measurement should you be more careful, the length or the diameter? Why?
Suppose that the current I (amperes) in an electrical circuit is related to the voltage V (volts) and the resistance R (ohms) by the equation I = V/R. If the voltage drops from 24 to 23 volts and the resistance drops from 100 to 80 ohms, will I increase or decrease? By about how much? Is the change
If a = 10 cm and b = 16 cm to the nearest millimeter, what should you expect the maximum percentage error to be in the calculated area A = πab of the ellipse x2/a2 + y2/b2 = 1?
Let y = uν and z = u + ν, where u and ν are positive independent variables.a. If u is measured with an error of 2% and ν with an error of 3%, about what is the percentage error in the calculated value of y?b. Show that the percentage error in the calculated value of z is less than the
Test the functions for local maxima and minima and saddle points. Find each function’s value at these points.ƒ(x, y) = 5x2 + 4xy - 2y2 + 4x - 4y
Test the functions for local maxima and minima and saddle points. Find each function’s value at these points.ƒ(x, y) = 2x3 + 3xy + 2y3
Test the functions for local maxima and minima and saddle points. Find each function’s value at these points.ƒ(x, y) = x3 + y3 + 3x2 - 3y2
Test the functions for local maxima and minima and saddle points. Find each function’s value at these points.ƒ(x, y) = x4 - 8x2 + 3y2 - 6y
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = x2 + xy + y2 - 3x + 3yR: The triangular region cut from the first quadrant by the line x + y = 4
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = x2 - y2 - 2x + 4y + 1R: The rectangular region in the first quadrant bounded by the coordinate axes and the lines x = 4 and y = 2
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = y2 - xy - 3y + 2xR: The square region enclosed by the lines x = ±2 and y = ±2
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = 2x + 2y - x2 - y2R: The square region bounded by the coordinate axes and the lines x = 2, y = 2 in the first quadrant
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = x2 - y2 - 2x + 4yR: The triangular region bounded below by the x-axis, above by the line y = x + 2, and on the right by the line x = 2
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = 4xy - x4 - y4 + 16R: The triangular region bounded below by the line y = -2, above by the line y = x, and on the right by the line x = 2
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = x3 + y3 + 3x2 - 3y2R: The square region enclosed by the lines x = ±1 and y = ±1
Find the absolute maximum and minimum values of ƒ on the region R.ƒ(x, y) = x3 + 3xy + y3 + 1R: The square region enclosed by the lines x = ±1 and y = ±1
Find the extreme values of ƒ(x, y) = x3 + y2 on the circle x2 + y2 = 1.
Find the extreme values of ƒ(x, y) = xy on the circle x2 + y2 = 1.
Find the extreme values of ƒ(x, y) = x2 + 3y2 + 2y on the unit disk x2 + y2 ≤ 1.
Find the points on the surface x2 - zy = 4 closest to the origin.
A closed rectangular box is to have volume V cm3. The cost of the material used in the box is a cents/cm2 for top and bottom, b cents/cm2 for front and back, and c cents/cm2 for the remaining sides. What dimensions minimize the total cost of materials?
Find the plane x/a + y/b + z/c = 1 that passes through the point (2, 1, 2) and cuts off the least volume from the first octant.
Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular cylinder x2 + y2 = 1 and the hyperbolic cylinder xz = 1.
Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the cone z2 = 2x2 + 2y2.
Let w = ƒ(r, θ), r = √x2 + y2, and θ = tan-1 ( y/x). Find ∂w/∂x and ∂w/∂y and express your answers in terms of r and θ.
Use the basic integration rules to find or evaluate the integral. | xe5-x² dx
Use the basic integration rules to find or evaluate the integral. x² √₁²³ - 27 dx
Use the basic integration rules to find or evaluate the integral. csc² (x + 8 4 dx
Let I = ∫40 f(x) dx, where f is shown in the figure. Let L(n) and R(n) represent the Riemann sums using the left-hand endpoints and right-hand endpoints of n subintervals of equal width. (Assume n is even.) Let T(n) and S(n) be the corresponding values of the Trapezoidal Rule and Simpson’s
Find the centroid of the region bounded by the x-axis and the curve y = e-c2x2, where c is a positive constant (see figure). y=e-c²₂² X
Use the basic integration rules to find or evaluate the integral. 2x x-3 - dx
Use integration by parts to find the indefinite integral. [x el-x dx
Decide whether the integral is improper. Explain your reasoning. л/4 Jo csc x dx
Use integration by parts to find the indefinite integral. x sec² x dx
What does it mean for an improper integral to converge?
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. *00 √3 1 (x - 1)4 dx
Use integration by parts to find the indefinite integral. x²ex/2 dx
Find the trigonometric integral. [COS (TX cos³(x - 1) dx
Find the trigonometric integral. sin x cos4 x dx
Find the trigonometric integral. [sin² sin² x cos³x dx
Find the trigonometric integral. π.Χ. sin². - dx 2
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. roo ex/3 dx
Find the trigonometric integral. X sec sec4=dx
Find the trigonometric integral. tan 8 sec 0 de
Find the trigonometric integral. x tan4 x² dx
Find the trigonometric integral. tan² x sec³ x dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 4 1 x(In x)³ -dx
Find the trigonometric integral. 1 1 - sin 0 de
Find the trigonometric integral. | (cos 20 ) (sin # + cos 0)2 dᎾ
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 00 In x X dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. roo 00 ex 1 + ex - dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. -00 4 16 + x² dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. roo 1³ dx (x² + 1)²°
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 00 1 et + ex dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. соs лx dx COS TX
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 10 00 sindx
Use partial fractions to find the indefinite integral. dx 9-x-zx 8-x
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. n/2 0 sec 0 de
Use partial fractions to find the indefinite integral. 5x – 2 -2 X dx
Use partial fractions to find the indefinite integral. x² - 2x + 1 dx
Use partial fractions to find the indefinite integral. x² + 2x x³x²+x-1 dx
Use partial fractions to find the indefinite integral. x³ + 4 3 x² - 4x dx
Use partial fractions to find the indefinite integral. 4x - 2 3(x-1)² dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 6 So √/36 13 1 /36-x- dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. Sexte 4 2 /2x²√√/x² - 4 J2 dx
Use partial fractions to find the indefinite integral. 4et (e2x - 1)(ex + 3) - dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. J4 x² - 16 x² dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 5 1 x²-9 1²5 xp: dx
Use partial fractions to find the indefinite integral. sec² 0 (tan 0) (tan 8 - 1) de
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 1 25x² dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 1 - dx x ln x
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 3 1 x√√x²-9 dx
Find the indefinite integral using any method. (sin 0 + cos 0)² de
Find the general solution of the differential equation using any method. dy 25 2 dx x² - 25 ||
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. dx (9 + x) x^ xp. 4 roo
Use integration tables to find or evaluate the integral. 1 1 + tan лx dx
Find the general solution of the differential equation using any method. dy dx 4x² 2x
Find the general solution of the differential equation using any method. y' = In(x² + x)
Find the general solution of the differential equation using any method. y' = √1 - cos 0
Find the area of the given region using any method. 1 y= 25 - x² 1 0.5 y 2 4
Evaluate the definite integral using any method. Use a graphing utility to verify your result. J2 (x² - 4) sin x dx (₂²
Find the area of the given region using any method. y=x√ √/3 - 2x 2 1 1 2 x
Find the arc length of the graph of y = √16 - x2 over the interval [0, 4].
Find the centroid of the region bounded by the graphs of the equations using any method.y = √1 - x2, y = 0
Find the capitalized cost C of an asset(a) For n = 5 years,(b) For n = 10 years(c) Forever. The capitalized cost is given bywhere C0 is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and c(t) is the annual cost of maintenance. fo Jo C = C₁
Find the capitalized cost C of an asset(a) For n = 5 years,(b) For n = 10 years(c) Forever. The capitalized cost is given bywhere C0 is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and c(t) is the annual cost of maintenance. fo Jo C = C₁
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. roo 1 x√√√x² - 4 2 x. =dx
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. 00 ex dx converges for a < 0.
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 8 1 In x x² dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. foº e-1/x x² - dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. roo x² In x dx
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 7 Jox-2 dx
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