Consider the following. C: counterclockwise around the circle  x2 + y2 = 49  from  (7, 0) to (−7, 0) (a) Find a parametrization of the path C. where r(t) =

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

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Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =&lt; −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

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Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

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Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: n exact form. Use symbolic notation and fractions where needed.)

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Q: Let z = (1+z)√√/50 — x² − y². - (A) Calculate the equation of the tangent plane at x = 3, y = 4. (B)…

A: z = (1 + x)50 - x2 - y2 The given function is of the form z = f(x) To calculate the equation of the…

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

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Q: Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right…

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Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Let f(x, y) = 5ex - Y. Find the equation for the tangent plane to the graph of f at the point (5,…

A: Given: fx, y=5ex-y. To Find: Equation of tangent plane to the graph of f at the point 5, 5.

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: 7x + 3y xy+1 (a) Compute Vf at the point (2,-4). 1. Let f(x, y) = (b) Compute the derivative of f(x,…

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: tangent plane

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Q: i y-jx x* + y* Q.5 (a) Compute |F.dr, where F and c is the circle x + y = 1 Use parametric equations…

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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