Find the Cartesian equation of the image of the line x = 2 under the mapping z → e z.  Sketch the image. If the pre-image point move on x = 2 from bottom to top, what is the orientation of the image point?

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A: Along the x axis we take value of angle and along y axis corresponding value of angle.

Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

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Q: Draw the line y = 2.x + 1 and its image under reflection in the y-axis.

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Q: 31. Figure 14.11 shows the contour diagram of g(x, y). Mark the points on the contours where (a) 8,…

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A: Consider the given equation as x=t3....(1) And y=t2....(2)

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Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

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Q: Which of the lines in Figure  are tangent to the curve?

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Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Find the equation in terms of x by substituting x=t in the given expression   y=t2-1=x2-1   To use…

Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

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Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Find the distance between the lines: r = + t r; = + s

A: Given: r1→=1,1,0+t1,6,2 and r2→=1,5,-2+s2,15,6 where a1=1,1,0 , a2=1,5,-2,b1=1,6,2, and b2=2,15,6 To…

Q: (a) At what point do the curves ri = (-4+t, -6 – 2t, 7+ 2t + t2) and r2 = (-5 – 2s, -4 +3s, 6 + s?)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) a. A(1,…

A: The graph is shown in next step.

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A: r2cos2θ=1

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Q: What is the equation of the line shown on t he gr aph below?

A: Given,           The line shown on the graph below :

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

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Q: Find the terminal point P(x, y) on the unit circle determined by the given value of t. Р(х, у) -

A: Given:

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Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: We have given the curve x=et ,y=e-t ,t∈ℝ.We have to find an equation in x,y whose graph contains the…

Q: Sketch the graph of y = h(t), where h(t)=uπ(t)−u2π(t),t≥0.

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Q: Find the missing coordinate of P given that PR is perpendicular to MN, which has a 4 and R(2,-9). 3…

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Q: Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2 Sketch the…

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Q: Plot the image of point P under a translation by 4 units to the left and 3 units down.

A: coordinate of given point P(-2,-4)

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: The given curve is rotated y = 3 - x2,

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Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: Find the points (x, y) in the unit circle satisfying the given condition 2 b. y = - =-²/ C. x = 4y 3…

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Q: Give the Cartesian equation of the locus of points P(x, y) given that P is 5 units from the point…

A: Any point on the Cartesian plane is represented as x, y. The locus is a set of points on the…

Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

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Q: If B is the midpoint of AC, with point A at (5, 2) and point C at (9, 0), what is the equation of…

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Q: The domain of ƒ(x, y) = In xy is points .(x, y) in the first quadrant

A: We have to tell about given statement.

Q: Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) e. Е(2.…

A: Solve by making graph

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem