At what points does the curve 2a cos t - a cos 2t, y = 2a sin t – a sin 2t x = ave vertical or horizontal tangents? Use this information to help sketch the curve.

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Obtain the equation of tangent by eliminating the parameter theta as follows.

Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the equation of the tangent line to the curve y 42 cos z at the point (, The equation of this…

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Q: Find the slope of the tangent to the astroid x = a cos30  y=  a sin30 in terms of 0

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Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: x = cos 2t 10. ly = sin 7t %3D

A: We will find the points at which the curve has vertical and horizontal tangents as following.

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

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Q: Find the slope of the tangent line for the curve r = 8 – 6 cos 0 when 0 4

A: Consider the provided curve, r=8-6cosθ where θ=π4. Find the slope of the curve. First we converting…

Q: Find an equation of the tangent line at the point specified.

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Q: Find the exact length of the curve r = sin 0 + cos 0.

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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: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: Use the guidelines of this section to sketch the curve.

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Q: Sketch the curve corresponding to r = 1 + cos θ.

A: we have to sketch the graph of the polar curve r=1+cos θ.

Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the points on the curve where the tangent line is horizontal and vertical. r = 1 − sin θ

A: In the question it is asked to find the points of tangent line (horizontal and vertical) to the…

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (7, –4t). The…

A: we have to find the equation of tangent

Q: At the given point, find the slope of the curve or the line that is tangent to the curve, as…

A: Use derivative

Q: Give the equation of the tangent line to the graph of 3sin y – In(e sech r) = tan-'(x²y) + 3 at the…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Sketch the curve y=sin(x)/(1+cos(x)).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0|? y=x+ y=0 TT…

A: Given that the curve is ey+cosx=1 and the point is π2,0. It is required to find the equation of…

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of…

A: The given paramedic equations are,

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: find the inflection point to the right of y-axis of the curve defined by the equation, y=x^2/2 +…

A: Given problem :- find the inflection point to the right of y-axis of the curve defined by the…

Q: Use the guidelines of this section to sketch the curve   y =sin x /( 2 + cos x )

A: Given: y=sinx2+cosx graph of given function can be drawn as below

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: Find an equation of the tangent line to the curve at each given point. x = 2 – 3 cos 0, y = 3 + 2…

A: Topic :- Application of Derivative

Q: Find the equations of the tangent lines x = 2 sin 2t, y = 3 sin t at the point where the curve…

A: Consider the given equation as x=2sin2t, y=3sint

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and passes…

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Q: find the slope of the tangent line to curve r= 7+ 2 cos theta when theta = pi/6

A: Given,           The slope of the tangent line to curve r=7+2cosθ when θ=π6

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: Determine the equation of the tangent line to (a) r = 2 sinθ at θ =π/6 (b) r =1 + cosθ at θ =π/2

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Q: Find an equation of the tangent line to the curve at the given point. (;-) TT y = sec(x) – 6 cos(x),…

A: We find the first derivative.

Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

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Q: Find the points on the curve r = 1– sin 0 - where the tangent line is horizontal or vertical.

A: To find out the points on the given curve, where the tangent line is horizontal or vertical.

Q: Find the equation of the tangent line to the curve tan(x+y) + sec(x-y) = 2 at the point (pi/8 ,…

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Q: 20. r = 3 cos 0 %3D

A: The given equation is; 20.       r= 3 cos(thetha). Repost the 21 and 22.

Q: What is the equation of the line tangent to the curve e+ cos(x) =1 at the point .0)? A y=0 B y=x -…

A: Explained below

Q: Find the points on the given curve where the tangent line is horizontal. r = 2 cos 0

A: Follow step 2 .

Q: Use the guidelines of this section to sketch the curve   y =sin x /( 1 + cos x )

A: Consider the curves: y=sinx1+cosx

Q: Find all the points where r = 2 + sin theta has vertical and horizontal tangent lines.

A: Consider the given question,Express the given polar equation in the parametric form as follows,

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

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Q: Find the equation of the tangent line to the curve r=cosθ at θ=π/4.

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Q: Find an equation of the tangent line to the curve at the given point. 1 + sin(x) y = (п, — 1) cos(x)

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