Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find a Cartesian equation of the curve.

Q: Find the exact length of the curve. y = ln(Sec x),   0≤ x ≤ π/4

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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: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

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

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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: O Find the equation of the line tangent to the curve at the given value of the parameter. x cost+…

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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: 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: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

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Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3,5).…

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

A: The curve whose tangent line at any point x,y is ex-cos x and passes through 0,4

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Q: Consider the equation x^(2)e^(y) +3y=1. a.) Find dy/dx by implicit differentiation. b.) Find the…

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

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

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Q: e cos at the Find the equation of the tangent line to the curve y = point (e?, 0).

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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: Given equations - x = sec2t-1                                       x = tan2t         .........(1)…

Q: Find the lengths of the curves x = ln (sec t + tan t) - sin ty = cos t, 0 ≤ t ≤ π/3

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

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Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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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: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

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

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

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 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…

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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: 3. Consider the curve given by r = 2+2 cos (0) where 0<0<2n. Find the slope of the tangent IT line…

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

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Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

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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: 1.   2. slope of tangent is dy/dx.

Q: Find an equation of the tangent line to the curve at the following point: y = z°e², (1,1/e) y =

A: SOLUTION-

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: 2. A curve C with equation y = sin2x 0 < x <5, has a stationary point, P. e3x dy (a) Find an…

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Q: Find an equation of the tangent line to the curve y = 4x sin (a) at the point (T /2,27). Express…

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Q: ind the second derivative (y") of the following function step-by-step and simplify the nal results:…

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

A: Given,         x=t-sint , y=1-3cost , t=π3

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: Q1- i) Show that cosh?x – sinh?x = 1 ii) Find the equation for the tangent line to the curve y = Vx…

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Q: Find the derivative of the following functions/parametric equations. 4. e2x cos y + y2 = 1

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Q: At what value of x does the curve 1„2 sin y = 3y +x² + 4x have a horizontal tangent? (Supporting…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: A. Find an equation for the tangent line to the curve x = -1 + sec? t, y = tan t %3D d2y at t =…

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