a) Plot the curve x^3 - 4xy + 2y^3 = 0 as x varies between -3 and 3 with the aid of the implicitplot command. b) Find dy/dx at all points (x,y) on the curve for which x = 1. c) Find the equations of the lines tangent to the curve at the points you found in part b. d) Plot the curve and the tangent lines on the same set of axes.

Q: Find the equation of the tangent line to the curve (a lemniscate) 2( +y) = 25(x - y) at the point (-…

A: 2(x2+y2)2=25(x2-y2)2(x4+y4+2x2y2)=25x2-25y22x4-25x2=-25y2-2y4-4x2y22x4-25x2=-25y2+2y4+4x2y2different…

Q: Find the equation of the tangent line to the curve y= (1+2x)2 at the point (2, 25). y = %3D

A: This question is based on application of Derivative.

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A:

Q: Find the equation of the tangent line to the curve y=2sin(x) at the point (pi/6, 1) in y=mx+b

A: Using equation of tangent formula.

Q: Find an equation of the line tangent to the curve y = (sin x)/1 + cos x at the point ( π/2 , 1)

A:

Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (G, 0)?

A: Given curveey+cosx=1Differentiate given curve with respect to…

Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: Find an equation of the tangent line to the curve at the given point. = sec X, (π/3, 2) y

A: The answer posted in the image would have been correct if the student had typed 23x instead of 23x…

Q: Find an equation of the tangent line to the curve at the given point. у %3D sec(x), (л/3, 2) 2nv3 y…

A:

Q: Find an equation of the tangent line at the point specified. y = excos2 x, x = π/4

A: Given curve is y=excos2x. To find the equation of the tangent line at the point x=π4. Solution: The…

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A: The standard form of the tangent line helps to find the required equation of the line. The standard…

Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: ,4 Consider the curve whose equation is x4 + y* + 3xy = 5. The dy slope of the tangeant line, at the…

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Q: Plot the astroid x = cos3 θ, y = sin3 θ and find the equation of the tangent line at θ = π/3 .

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Q: Find an equation of the tangent line to the curve at the following point:  y=4/1+e^-x, (0,2) y=?

A: We first find the slope of the tangent using the first derivative y=41+e-xy=4(1+e-x)-1…

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Find the equation of the tangent line to the curve at the given point.

A: To find the tangent at the given point on the curve, using derivatives

Q: Find the equation of the tangent line to x + y = 9 %3D at the point (2, v5)

A: Equation of tangent to any curve y = f(x) at a given point ( x1, y1 ) is given by           ( y - y1…

Q: Find the equation of the tangent line to the curve y = 6x cos x at the point (7, The equation of…

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Q: Find the equation of the tangent line to the curve y = 2 In (22 at the point (1, 2) . (Hint:…

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Q: Determine the equation of the line tangent to y = (sin x)²(cos x) at the point (5,0).

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Q: Find the equation of the tangent line to the curve at the given point. y = V2x + I, (4,3) y =

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Q: Find the equation of the tangent line of the curve y = sin x + cos x at the point A ( π ,√2 ) .…

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Q: Find the equation of the tangent line to the curve y = xVĩ at the point (1, 1). y =

A:

Q: The slope of the tangent line to the curve y at the point ( 5, is: The equation of this tangent line…

A: Given curve is : y=3x To find the slope of tangent at the point 5,35 and equation of tangent in the…

Q: Find the slope of the tangent line to the curve cos(3x−3y)−xe−x=−7π2e−7π/2 at the point (7π/2,3π).

A:

Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A: We can answer the question in the following steps.

Q: Find the equation of the tangent line to the curve y = 2 In(x - 26) at the point (3,0). %3D y =

A:

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: Find the equation of the tangent line to the curve y 2x cos x at the point (п, — 2т). The equation…

A: We will find the equation of tangent line.

Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²) + 1 at (x,y)= (…

A:

Q: Find an equation of the tangent line to the curve y=sin(3x) + cos(4x)   at the point (pi/6),…

A: Given equation is y=sin(3x) + cos(4x).

Q: Find an equation of the tangent line to the curve y = 3 arccos (1,4 π). Select the correct answer.…

A: Find an equation of the tangent line to the curve y= 3cos-1(x/2) at the point (1,4π) .

Q: Find the equation of the tangent line to the curve y = 8 sin z at the point (, 4). 6

A:

Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²)+1 at…

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Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

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Q: Find the equation of the tangent line to the curve y = 4x coS T at the point (7, - 47). The equation…

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Q: Find an equation of the tangent to the curve given by tan(0), y = sec(0) at the point (x, y) = (1,…

A:

Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: It is given that the x coordinate increases at a steady 10 m/sec. dxdt=10msec. The equation of…

Q: find the equation of the tangent line to the curve at the point corresponding 4o the given value of…

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

Q: Find the equation of the tangent line to the curve: sin (2x + y) + cos-'(x +2y) 6 at the point Enter…

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Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

A:

Q: How do you find the equation of the tangent line to the curve y= 2 tan(x) at the point (pi/4, 2)…

A: To find the equation of tangent line to the curve y= 2 tan(x) at the point (pi/4, 2).

Q: Find the equation of the tangent line to the curve y 6x cos x at the point (π, = The equation of…

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Q: (a) Find the equation of the tangent line to the curvey 2 sec x – 4 cos x at the point (÷, 2)

A: Tangent line to the curve y=f(x), where f(x) is a function of x at point x0, y0is given by:…

Q: Find the equation of the line tangent to the curve 2(z² + y°)* = 25(z² – y²) at the point (3, 1).…

A: Suppose a line passing through with slope  m then equation of line is .

Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…