Homework Answers
1.) Given: x=5cost and y=2sint a. Sketch a graph of the parametric curve by eliminating the...
1.) Given: x=5cost and y=2sint a. Sketch a graph of the parametric curve by eliminating the parameter and Label orientation. Show all work. b. Determine dy/dx and d^2y/d^2x Show work and simplify your answers. Express answers in terms of “t”
Solve C and D part please Sketch the curve represented by the parametric equations (indicate the...
Solve C and D part please
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.(Can you name the curve?) (a) r = sin 0, y = cos, - SOST (b) x = 4 sect and y = 3 tant 3 3 (c) r=-1+ z sint and y = cost for -A <t <3 (d) x = cosht and y cosh 3t (no need to sketch...
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t))...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
Sketch the graph of the resulting function. 2. Solve a" +x = 8(t - ) -...
Sketch the graph of the resulting function. 2. Solve a" +x = 8(t - ) - 8(t-2r), z(0) = 0, z'(0) = 1. Sketch the graph of the result ing function. 3. Find a first order system corresponding to the scalar equation and find its general solution. (a) y"-44y= 0. (b) t2y"- 4ty+ 4y = 0, t > 0. (It general solution is of the form y(t) = ct+ cztt.) 4. Find the general solution to the system r'= Ar,...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
solve both problems For the function y = x2+8 3, find and graph the coordinates of...
solve both problems
For the function y = x2+8 3, find and graph the coordinates of any local X-3 extreme points and/or inflection points. 4 Sketch the function y xv4- x2. What, if any, are the x-intercepts. Is the graph symmetric to the x-axis, the y-axis, or the origin? What is the domain and range?
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integrationRin Figure 3.(b) By completing the
limits and integrand, set up (without evaluating) the integral in
polar coordinates.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b)...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
Solve the given symbolic initial value problem and sketch a graph of the solution y" +...
Solve the given symbolic initial value problem and sketch a graph of the solution y" + 2y =60(1-4): y0)=0, y(0) = 2 Solve the given symbolic initial value problem. y(t) =
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1 Determine the nullclines, sketch the vector field, and then...
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.)
r(0) 2, y(0)1
Solve C and D part please
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.(Can you name the curve?) (a) r = sin 0, y = cos, - SOST (b) x = 4 sect and y = 3 tant 3 3 (c) r=-1+ z sint and y = cost for -A <t <3 (d) x = cosht and y cosh 3t (no need to sketch...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
Sketch the graph of the resulting function. 2. Solve a" +x = 8(t - ) - 8(t-2r), z(0) = 0, z'(0) = 1. Sketch the graph of the result ing function. 3. Find a first order system corresponding to the scalar equation and find its general solution. (a) y"-44y= 0. (b) t2y"- 4ty+ 4y = 0, t > 0. (It general solution is of the form y(t) = ct+ cztt.) 4. Find the general solution to the system r'= Ar,...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
solve both problems
For the function y = x2+8 3, find and graph the coordinates of any local X-3 extreme points and/or inflection points. 4 Sketch the function y xv4- x2. What, if any, are the x-intercepts. Is the graph symmetric to the x-axis, the y-axis, or the origin? What is the domain and range?
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integrationRin Figure 3.(b) By completing the
limits and integrand, set up (without evaluating) the integral in
polar coordinates.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
Solve the given symbolic initial value problem and sketch a graph of the solution y" + 2y =60(1-4): y0)=0, y(0) = 2 Solve the given symbolic initial value problem. y(t) =
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.)
r(0) 2, y(0)1
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