please write neatly and no script!
please write neatly and no script! 4. (10 points) Describe the surface given by the equation...
please write neatly and no script!
8. (10 points) (a) Using rectangular coordinates, set up an iterated integral that represents the volume of the solid bounded by the surfaces z = x2 + y2 +3, z = 0, and x2 + y2 = 1. (b) Evaluate the iterated integral in (a) by converting to polar coordinates.
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7. (10 points) For the following iterated integral, sketch the region of integration, then switch the order of integration and evaluate the new iterated integral. 1 •1/2 SL e-22 dx dy. y/2
#4 part a and b please write solutions neatly
4. (20 points) (a) (15 points) Find the general solution of the linear differential equation y-by's on (0,-) using variation of parameters 4. (b) (5 points Use your answer to 5.42) to solve the initial-value problem 32-64 += 310=2,80)=0.
Consider the parametric surface given in cylindrical coordinates by the equation x2 +y2 < 1 and below the plane :-2T. 1 Credit disk 0 3. θ above the unit -1 Using the parametrization g(r,0) = (r cose, r sina, e, o s r UATE the integral to compute the surface area. e 1, 0 2r, set up BUT DO NOT EVAL-
Consider the parametric surface given in cylindrical coordinates by the equation x2 +y2
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6. (10 points) For each of the following, write the given equation in “standard form” (by completing the square or otherwise), describe all traces and sketch the surface in R3. (a) 1672 – 4x2 + z2 = 16 (b) 5x2 + 4y2 – 20x + 8y – z=-4
#1 part a and b please write solutions neatly
1. (16 points) Determine whether the given set of functions is linearly dependent or linearly independent on the indicated interval. Justify your answers. (a) (8 points) f(x) = x + 2 cos?x, f?(x) = 3sin?x, f(x) = x+2 on (-0,0). (b) (8 points) f (x) = ed" and 12(x) = e 4s are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,0).
#2 part a b and c please. please write solutions neatly
2. (27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution y, of the nonhomogeneous equation. Do not solve for the undetermined coefficients in y, (a) (10 points) y" - 9 - 22 y 3x2 (b) (10 points) y" - 4y' + 29y = 8r sin 3x 3 2. (c)points) Find a homogeneous linear...
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4. Consider the differential equation y (y 1)(y2)(y-3) (a) Sketch a solution to the equation for the initial conditions y(0) = 1/2 and y(0) 3/2. (b) Let o be the solution to the equation passing through the point (0, 2.99). Find lim o(t). (Be sure to explain your reasoning.) t-oo
Introduction to Analysis.
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4. (10 points) Prove that two real numbers a, b satisfy a<b for every e > 0, a <b+€
Use matlab and write script: Please use n = input('Enter the value of n :') not the function command. Consider the following equation 6a + 9b + 20c = n The variables a, b, and c can be thought of as the number (non-negative integers) of 6’s, 9’s, and 20’s in n. Note that for a given n, there might be one, multiple, or no solutions for a, b, and c. For example, n = 15 → a = 1...