The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the gradient, when t = 1. dx

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = 2t3 -…

A: Topic- application of derivatives and tangent equation

Q: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

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Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

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: A particle moves along a straight line with velocity function  v(t) = sin t - cos t and its initial…

A: Given that a particle moves along a straight line with velocity function vt=sint-cost and its…

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find the second derivative of the parametric equation ; x = t3 + 1, y = 4t2 −4t.

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Q: The parametric equation of a curve is given by x= cost, y= sint− cost, 0 ≤ t ≤ 1 . Without…

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Q: Find the derivative dy/dx of the polar function r=3+2cosθ at θ=π6.

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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: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

Q: Consider the parametric curve given by x = t2 + 5, y= e* est + 2t. 3t Find the slope of the tangent…

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Q: Find dy/dx and d2 y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given, x = cos3 θ, y = sin3 θ Parameter θ = π/4

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 parametric equations of a curve are given by = In (Vi +1) and y = cosh" (21). dy Find the…

A: The derivative of the function u=f(v) is the measure of how fast the function f is changing with…

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

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Q: Find the exact slope of the tangent line to the parametric curve at the point where y = 2 sin(t) t =…

A: x=8 cos (t) y=2 sin (t)

Q: Find an equation of the tangent line for.10 a curve defined by the following parametric equations x…

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Q: 1. Evaluate the dy for parametric equations x = 3t³ - 3 and dx y = 3t² - 6t using parametric…

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Q: Find a standard equation for the tangent plane and parametric equations of the normal line at the…

A: Introduction: If F(x,y,z) is a differentiable surface at the point (x0,y0,z0), the tangent plane to…

Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

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Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

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: The parametric equations of a curve are given by 1 = In (Vi +1) and y= cosh(2t). dy when t = 1. dr…

A: According  to question given thatx=ln(t+1)y=cosh-1(2t)

Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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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: A curve is described parametrically as x = e' sint, y = e'cost, – o <t< ao. Find the equation of the…

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Q: Find the 3rd derivative of the function given by the parametric equations x=1+t2, y=t−t3 at t=1.

A: Differentiate x and y with respect to t.

Q: Find an equation for the tangent plane to z = f(x, y) at (3,-2) if the differential at (3,-2) is df…

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Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: What is the equation for the line tangent to the parametric curve I = 4 sin(2t) y = 4 sin(t) at t=…

A: Explanation: Given that: x=4sin2ty=4sintt=π6or 30° Concept used: The standard equation of line…

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: 2. * (t) = t lnt and Y (t) = (t – 1)?

A: We need to find the first and second order derivative of the given function. This can be done as…

Q: A curve is defined by the parametric equations: x(t) = e' cost, y(t) = e' sint dy d²y Determine and…

A: The tangent line to the curve in parametric form is given as follows

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative

Q: Calculate the derivative dy for the parametric equation x=t7+t³+ln(5t + 1), y = e4t²_ +t6 giving…

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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: VI. x = v1 - t , y = t³ – 3t

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