5. If мая abstract manifolds, PEM. f a) Define TpM and dfp, where M²₂N is smooth map beton by dfp: TM> TR (N) is linear. are

Q: 5. Give an example of a curve C C xy plane so that its curvature as a space curve is different from…

A: The given: A curve  in the -plane defined by parametric equations and .The objective: To…

Q: ARST Is translated so that point R (-2, 1) Is mapped to point R' (2, -4). Which ordered pair best…

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Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: What is the image of a horizontal line y = k € R under the mapping W = 2²?

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Q: Suppose that Find the Jacobian Metrix for map.

A: Given y1=x1x2-x2x4y2=x12-x42y3=x1x2x3x4

Q: 3. Sketch the parallelogram spanned by (2, 1, 0) and (-3, 1, 0) in the xy plane and find its area.

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Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: б. (a) Sketch the level curves z = k for k = 0, 1, 2 if z = x2 – y?.

A: The level curves of a function f of two variables are the curves with equations f(x, y) = c, where c…

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Let P, Q be two points on the sphere of radius 1. Assume that P ≠ -Q. Show that there exists a curve…

A: Given P and Q be two points on the sphere of radius 1 P ≠ -Q. We need to show that there exists a…

Q: 7. Consider a line in 2-dim space y = ax + b and a given point (ro. 30) not on the line. Please…

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Q: formela for the fun thn yoga) Con súto of two line 2) Write cmula whose as in fguve the f Mawing : 6…

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Q: 1.) Obtain the general solution of the differential equation dx – (1 + 2x tany) dy = 0.

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Q: (4) 2 What is the square of the (minimum) distance between W and P? Let W Span< = -2 be a plane in…

A: Given that

Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Sketch the following sets of points in the x-y plane. {(x, x^2): x is in R}

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Q: Prove that a line intersects a paraboloid at' two points which may be real or imaginary.

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center of…

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: Show that the transformation w = maps the circle x² + y² - 4x = 0 into the straight line 2z + 3 4 Z…

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Q: Which of these describes the contour curves/level curves of the function f(x, y) = (x² + y²)'/3 +…

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Q: Show that the two planer diagram represent the homeomorphic surfaces

A: Given:-                 Show that the two planer diagram represent the homeomorphic surfaces