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Problem 4 (20 points): Determine the area of the region below the parametric...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts)...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
1. Find the area of the region bounded by the parametric curve x = 2 sin?...
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
please help me and show all the steps and make sure it's correct [10 pts] 3....
please help me and show all the steps and make sure it's
correct
[10 pts] 3. Find the area inside the asteroid given by the parametric equations x = 4 cos' (t) and y = 4sin) for Osts 27. Show the setup of the integral and use your TI84's "fnint command to find the area.. [10 pts.) 4. Find the arc length of the asteroid given by the parametric equations x = 4 cos' (t) and y = 4 sin()...
4. Consider the area of the region that lies inside the curve given in polar form)...
4. Consider the area of the region that lies inside the curve given in polar form) by r = 6 sin(@) and outside the cardioid given by r=2+2 sin(0). (a) (3pts) Set up but do not evaluate an integral(s) which represents the area of this region. (b) (3.5pts) Evaluate this integral to determine the exact area of this region. (Hint: you will need to use a trig, identity)
A curve called the folium of Descartes can be represented by the parametric equations shown below. 912 1 + 13 9t and y 1 + t3 (a) Convert the parametric equations to polar form. 9 cos( 0)sin (6)...
A curve called the folium of Descartes can be represented by the parametric equations shown below. 912 1 + 13 9t and y 1 + t3 (a) Convert the parametric equations to polar form. 9 cos( 0)sin (6) c())3 (sin(0)5 cos(θ) ),+ (sin( (b) Sketch the graph of the polar equation from part (a). 71/2 0.10 0.05 -4 0.05 0.10 0.15 -0.05 0.05 π/2 10 1.0 0.5 0.5 -0.5 10 -0.5 (c) Use a graphing utility to approximate the area...
Sketch the region and use a double integral to find the area of the region inside...
Sketch the region and use a double integral to find the area of
the region inside both the cardioid r=1+sin(theta) and
r=1+cos(theta).
I have worked through the problem twice and keep getting (3pi/4
- sqrt(2)). Can someone please explain how you arrive at, what they
say, is the correct answer?
Sketch the region and use a double integral to find its area The region inside both the cardioid r= 1 + sin 0 and the cardioid r= 1 + cosa...
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1)...
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slo...
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2.
Problem 3 (12 points) The curve with parametric equations...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Problem 5. Prove that parametric equations: x a-cosh(s) (a > 0) or back half(a < 0) of hyperboloid of one she...
Problem 5. Prove that parametric equations: x a-cosh(s) (a > 0) or back half(a < 0) of hyperboloid of one sheet: Χ t), y b-sinh(s) cos (t) zc-sinh(s) sin( t), (x,y,z) lies on the front half L" a2 b2 c2 Problem 6 What graph of this Compute the arc length : rit)- < sin t, cos t, 2Vt', when 0<t < function: a) Compute the arc length : re)-3cos(9) and 0 < θ < π/2 b) Problem 7. Find parametric...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
please help me and show all the steps and make sure it's
correct
[10 pts] 3. Find the area inside the asteroid given by the parametric equations x = 4 cos' (t) and y = 4sin) for Osts 27. Show the setup of the integral and use your TI84's "fnint command to find the area.. [10 pts.) 4. Find the arc length of the asteroid given by the parametric equations x = 4 cos' (t) and y = 4 sin()...
4. Consider the area of the region that lies inside the curve given in polar form) by r = 6 sin(@) and outside the cardioid given by r=2+2 sin(0). (a) (3pts) Set up but do not evaluate an integral(s) which represents the area of this region. (b) (3.5pts) Evaluate this integral to determine the exact area of this region. (Hint: you will need to use a trig, identity)
A curve called the folium of Descartes can be represented by the parametric equations shown below. 912 1 + 13 9t and y 1 + t3 (a) Convert the parametric equations to polar form. 9 cos( 0)sin (6) c())3 (sin(0)5 cos(θ) ),+ (sin( (b) Sketch the graph of the polar equation from part (a). 71/2 0.10 0.05 -4 0.05 0.10 0.15 -0.05 0.05 π/2 10 1.0 0.5 0.5 -0.5 10 -0.5 (c) Use a graphing utility to approximate the area...
Sketch the region and use a double integral to find the area of
the region inside both the cardioid r=1+sin(theta) and
r=1+cos(theta).
I have worked through the problem twice and keep getting (3pi/4
- sqrt(2)). Can someone please explain how you arrive at, what they
say, is the correct answer?
Sketch the region and use a double integral to find its area The region inside both the cardioid r= 1 + sin 0 and the cardioid r= 1 + cosa...
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2.
Problem 3 (12 points) The curve with parametric equations...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Problem 5. Prove that parametric equations: x a-cosh(s) (a > 0) or back half(a < 0) of hyperboloid of one sheet: Χ t), y b-sinh(s) cos (t) zc-sinh(s) sin( t), (x,y,z) lies on the front half L" a2 b2 c2 Problem 6 What graph of this Compute the arc length : rit)- < sin t, cos t, 2Vt', when 0<t < function: a) Compute the arc length : re)-3cos(9) and 0 < θ < π/2 b) Problem 7. Find parametric...
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