Consider the following. x = sinh(t),    y = cosh(t) (a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Q: a) Plot the parametric curve x=1 – sin t, y=1+ cos t with 0 <t< ™. b) Determine the equation of the…

A: Given: For the curve x=1-sin(t) t 0 π/2 π x 1 0 1

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A:

Q: Find the equation of the tangent line to the curve y = 5x cos T at the point (T, – 57). The equation…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Given: The parametric equation of curve as To determine: The cartesian equation of curve by…

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: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: To find: The equation of tangent to the curve and also find d2ydx2. Given: The functions are x=cos…

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: Let C be the graph of the equation In(3y – 2e") = sinh“(Tx) – tan(y – 1). | dy (a) Find dr (b) Find…

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Q: 1. Consider the curve C: r(t) = (t - sin t)i + (1– cos t)j, 0StS 2. %3| | (a) Find an equation of…

A: Since solve the first question for you. If you wanting any specific question to be solved then…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t 15)…

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

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

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Q: Find the equation of the tangent line to the curve y = 4 sin x + 2 cos a at the point (0, 1/2). The…

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Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

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

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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: X= cos t, y= sin t; t= 6

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Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

A:

Q: 3. Find the slope of the tangent line to the polar curve, r = 2 cos 0, at the point specified by 0 =…

A: Given:        r=2cosθ at the point specified by θ=π3.

Q: 3) Consider the curve parameterized by x = csc t, y = cot t, 0 < t < t. Determine the equation of…

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

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Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

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Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Tangent line for a curve at a point is a line which just touches it and is "parallel" to the curve…

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

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

A: To find the slope of the tangent we need to find dy/dx Then find dy/dx at t=pi

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = 2 cos(t), y =…

A: Given parametric equations are

Q: I and y are related by 16 ye8 xy = sin (5 z). (a) Find dy at the point (0, 0). (b) Find the equation…

A: since given that x and y are related to each other as 16ye8xy=sin(5x)

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

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

A: take derivative take

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

A:

Q: Find the length of the curve y = ln (sin x),  pai/6&lt;=x&lt;=pai/2.

A: The given curve is,

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

A: First, to find equation of the tangent to the curve by without eliminating method:

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

A: 1.   2. slope of tangent is dy/dx.

Q: Find the equation of the tangent line to the curve 1 y = 3 sin z + 4 cos a at the point (0, 1/4).…

A: Given:     y = 1 / ( 3 sinx + 4 cosx ) Point: ( 0 , 1/4 )

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

A: Given,  x = t cost  y = t sint    We have to find the equation of the tangent at the point t = π.

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

A: Our objective to find the cartesian equation of the curve.

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

A:

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

A: Given that, x=tcost, y=tsint, t=π. Find the value of x and y by substituting the value of t in given…

Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

A:

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

A:

Q: For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the…

A: Given that the parametric equations of a curve is                               x = cos (t) ,   y =…

Q: 4 cos(t) { Find the slope of the tangent line to the parametric curve at the point 1 sin(t) 6 Y =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.