Question 15 If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y=x' +k, then k is А) 1/2 В) -1/2 1/4 -1/8

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Explanation :  Given that x= 3cost + sint y = e^2t

Q: Question 1 Consider the curve defined by 2y3 + 6x2y - 12x² + 6y = 1. dy 4х - 2ху (a) Show that dx x2…

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Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

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Q: Question 12 Find the moment of inertia of the region between the parabola y = 9 - x2 and the line y…

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Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes…

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Q: Question 3 Express the curve by an equation in r and y given r(t) = sec² (t) + 2 and y(t) = 5 +…

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Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent to a curve at a point is a line that just touches the curve at that point and in some sense…

Q: Question 2 Express the curve by an equation in x and y given x(t) = 11 – sin(t) and y(t) = cos(t).…

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Q: 1 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 2 sin(t)

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Q: 17. If the curve C is given by x= 3t² +1, y=4t, z = e, find the equation of the tangent line at the…

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Q: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê

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Q: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

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Q: Question 3 Express the curve by an equation in x and y given x(1) = sec? (t) + 2 and y(t) = 3 +…

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Q: re poinit Cur 8X° + 22X 24X e tangent line is parallel to the x-axis? . (1,0) (2,1) (3,0)

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Q: Question 2 Find an equation for the line tangent to the curve at the point defined by the given…

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Q: Question 4 Express the curve by an equation in a and y given #(t) = sin(t) and y(t) = 9 + cos? (t).…

A: Given functions are, xt=sintyt=9+cos2t

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: Question 2. (a) Find the tangent plane and normal line of the surface f(x,y,z) = x³ + y² – 6z + 5 =…

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

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Q: 1. Consider the curve given by the equation y3 – xy = 2. It can be shown that dy %3D y dx 3y2-x (a)…

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Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent line at a point will be given by slope at that particular point and one passing point for…

Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: Question 3 Find the value of J sinydx+ (xcosy-sinyldy, where Cis any curve from (2,0) to (1, T). Ca…

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Q: Question 6 Find the area 2 y=x²-3 between the curves and y=x+3

A: In this question, we will find the area of the region bounded by the given curves.

Q: Question 8: The curve C in the ry-plane is parameterized by r (t). Find a parameterization of the…

A: Given:r→'t=4, 4e2t, 2costr→0=0,1,0

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Which of the following is the equation of tangent line of the curve that is given 2t by parametric…

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Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: A b. C find an equation of the tangent to the curve at the given point (T/6,1) 4 sin ² x y = + y =…

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Q: Question 12 Find a at time t = 1 for the plane curve r(t) = 4t²i+ 3tj. Round your answer to three…

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Q: Question 3 Find the point(s) of intersection of the curves r = 6 and r = 12 sin e OA 6 * (6.5)(6) 3…

A: To find the intersection of the curve r=6 and r=12sinθ

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: QUESTION 3 Evaluate fds, where f(x,y) 2x +3y and C is the counterclockwise curve around the circle…

A: Given function is, fx,y=2x+3y The equation of circle is, x2+y2=4

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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Q: QUESTION 14 Which one of the following points lies on the curve r= sin 0-5. (5, 0) o (5, 2n) o (-5,…

A: In this we find that point which lies on the given curve.

Q: Question 8 Find the coordinates of the point(s) on the curve y = Va + 4 that are closest to the…

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Q: Problem 13. Determine the acceleration of a car moving on a curved path from point A (as the…

A: y=-1.5x2+3

Q: Problem 2. Consider the curve r(t) = (e¬t cos(t), e¬t sin(t), 5 – 5e¬t) for t > 0. a) Find the…

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Q: Question 21 Find the equation of the tangent line to y = x = 1. at A y - Vi = - Vi (x – 1) B VE (x -…

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

A: We have to find

Q: A curve is described parametrically as x = e' sint, y = e'cost, – o <t< ao. Find the equation of the…

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Q: Let C be the graph of the equation In(3y – 2e") = sinh (ma) - tan(y- 1). dy (a) Find da (b) Find an…

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Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

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Q: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

Q: Question 2. Find from the origin (0, 0) the direction of steepest increase of the function f (x, y)…

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Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem

Q: B The equation of a curve is y = cotx - 8 cos x, 0<x< π, find the coordinates of the points on the…

A: If the equation of the curve is given y=f(x)  Then we find dy/dx and then equating to 0 we get the…