Consider the following. x = t4, y = In(t) (a) Eliminate the parameter to find a Cartesian equation of the curve.

Q: ind an equation of the tangent to the curve parameter. 18. z = t, y = t² – 1; t= -4

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: (a) Find the slope of the tangent line to the parametric curve x = t/2, y = t 2 + 1 at t= −1and at t…

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Q: 2. Eliminate the parameter and find the equation of the curve in x,y Curve: x=1-sin?t, y= cost, 0 <t…

A: topic - equation of curve in x,y

Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: (c) Find dy/dx at t = T/3. (d) Include in sketch for (a) the tangent line to the curve at t = T/3…

A: We have to find the equation of tangent line.

Q: 5) Sketch the curve X = e', Y = e?t + 1

A: Given, The curve  X = et  and  Y = e2t+1 We have to sketch the curve.

Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: 1) Find the length of the curve; y = e" from r= 1 toI = 2.

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

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: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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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: Explanation of the answer is as follows

Q: Find an equation of the tangent to the curve given by y = t – In(t²) at the point corresponding to t…

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Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

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: Q3/Find the tangent to the curve x+ xy+ y' = 1 at (1,-1).

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Q: (a) Find the slope of the tangent line to the parametric curve x = t² + 1, y = t/2at t = −1and t = 1…

A: Given,                          x=t2+1,   y=t2,    and               t=-1,            t=1

Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

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Q: Consider the curve parameterized by x(t) = 2(t²-1), y(t) = 5e²t, tER Determine an equation of the…

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Q: What is the formula for the slope dy/dx of a parametrized curve x = ƒ(t), y = g(t)? When does the…

A: Given parametric curves are

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

A: The solution are next step is

Q: 1. Find the equation of the tangent line to the curve: x = Vt, y = e² at t=1. d?y at t=1 for the…

A: Solve by using differentiation.

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…

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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: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

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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: The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y)…

A: Given query is to find the point of horizontal tangent.

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…

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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: Equation of tangent line at (x0,y0) (y-y0) = m(x-x0)

Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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Q: Find a parametric equation for the tangent line to the curve defined by r(t) = when t = 1.

A: Given is the equation of a 3-dimensional parametric equation, to find the equation of the tangent we…

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Q: Q7// Find tangent and normal equations of the curve x³ + y3 – 9xy = 0 at points (4,2) and (2,4).

A: The slope of a curve at the point (x1, y1 ) is given by;…

Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

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

Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x ey cos z at…

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Q: -38x^8+10x^76y+y^9=-27, find the dy/dx. Now find the tangent line to the curve (1,1). Write in…

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Q: 1. Find an equation of the tangent to the curve, x = t + 1, y = t4 + t corresponding to t = - 1.

A: To find the equation of tangent for following curve x = t3 +1    .... 1 y = t4 + t    ..... 2 AT t =…

Q: x = VE, y = t? – 2t; t = 16

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

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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: x=et , y=t-lnt2,  t=1 Differentiating with respect to t, we get dxdt=detdt  &amp;…

Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: Write the equation of the tangent line in Cartesian coordinates for the given parameter t. x = eVE y…

A: at t=1 x=e1=e1=ey=1-ln(12)=1-ln(1)=1-0=1 tangent point (x1,y1)=(e,1)equation of tangent line…

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

A: Using formula of equation of tangent line.