1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the mapping = -iz?. W = 3. Draw L and its image.

Q: Sketch the graphs of the following cylinders. Properly identify a cross-section on the appropriate…

A: Given: Let's consider the given equation and graph the following cylinders. y=2x-4

Q: (a) find a parametrization of the path C, and (b) evaluate (r? + y?) ds.

A: Here we have to find the Parameterization of path C, Counterclockwise around the circle x2+y2=1 from…

Q: The distance from (6,-5, 1) to yZ-plane is OA 6 /26 OC 1 O D. 62 OE 5 В.

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Q: Graph the curve r = 1 - cos θ in the Cartesian xy-plane

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Q: Find the length of the curve r= cos'(8/3). OsesT/4

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Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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Q: Give for the line through the point a vectur parametri? eauatiun Cl-2) that is -4,41345pendicular'to…

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Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: Find a parametrization for the curve described below. the line segment with endpoints (1, – 4) and…

A: Given:   Endpoint : ( 1 , -4) and ( -2 , -7)

Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Find Df and Duf to:- XZ on the point (,,1) inthe direction of V = 2i -3j+6 K. %3D soLiin ansi- lo

A: Directional derivative of the function.

Q: Find three different parametrizations of the graph of y = x3.

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Q: Given show =5 how dy %3D

A: differentiate y with respect to x .

Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

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Q: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

Q: Ex: Let tanh u = – determine the values of the remaining five hyperbolic functions.

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Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (5 - 1) and…

A: Given point :( 5 , -1 ) (10 , -6 )

Q: Find the length of the following two-dimensional curve. (21+1,3/24 r(t) = 2 3 for 0 sts6 L- (Type an…

A: To find The length of the given two dimensional curve.

Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

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Q: Find the length of the following three-dimensional curve. r(t) = (5+ 4t,9-3t, - 6+2t), for 1sts6 L =…

A: length of the curve r(t) is L=∫ab∥r′(t)∥dt

Q: Demonstrate that the circles (x – 2)? + y² = 2 and x? + (y – 2)2 = 2 share tangent at point (1, 1),…

A: Here we will apply the concept of finding the equation of tangent to the two circles at point (1,1).

Q: |A" |= |B |,implies that A=B" %3D ylgn ihi

A: Use the property of vector and their modulus.

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: a. The perpendicular bisector of JK is the perpendicular to f that passes through P. b. Draw an arc…

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Q: at.p.(I,.0)..and. the directiun. in. whichit.occurs

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Q: Let C be parametrized by x = t and y = 6t for 0 <t < 4. Find the length L of C. L = (In this case,…

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Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: | the parametric equatioin for e line segment between a7) and (3,3)

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Q: The equation of the tangent plane to the surfice. -yeV + = 0 at the point (0,1,1) is ar + by + cz =…

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Q: Evaluate fc (2 +x 2y ) ds, where is the upper half of the unit circle x2 y2 =1

A: We have to evaluate ∮C2+x2ydS   where C is the upper half of the unit circle x2+y2=1

Q: 8- of What is the value of (z + e22) dz, where C is the positiv C oriented circle |z - 1= 1 in the…

A: Since z-1=1 ⇒z-12=1⇒z-1z-1¯=1⇒z-1z¯-1=1⇒zz¯-z¯-z=0⇒z¯z-1=z⇒z¯=zz-1

Q: 28, Find the equa tion of arcle with Centre c(2;3) and touches the x-axis.

A: By using equation of circle formula, we find the required equation of circle.

Q: Graph and locate the foci. (z- 3) , (y+1)² = 1 %3D 25 36 Posted Wed Mar 31, 2021 at 12:17 pm…

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Q: yepriate trigonomic subititution to rewrite the intya) U se in the form E sec'e de

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

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Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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Q: Point P is the centroid for AMNO. calculate MO if MR = 13. Round to the nearest tenth if necessary.…

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Q: Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) =…

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Q: A rectangular building lot 1s 3 time O Jong Eoction that models its A in terms of it's wicth w.

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Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

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Q: Find the areas of the regions Inside the six-leaved rose r2 = 2 sin 3θ

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