1. Calculate the derivative dy/dx for the plane curve defined by the equations: x(t)=t²-4t, y(t)=2t³-6t, for -2Sts3 and locate any critical noint on itc granh

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

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Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t3/2 at t = 1. Also…

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Q: 3. y = C( Sec x+ tan x)

A: Note: we get orthogonal trajectories of families of curves by 1.differentiating  curve 2. Then…

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: (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: Find the derivative dy/dx of the hyperbolic spiral r=aθ.

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Can you please solve these two sub problems and show all of the steps and say the correct letter

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Consider the curve in the xy-plane repre- sented by = e' and y = The slope of the line tangent to…

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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: 17. The equation of the tangent line to the curve y = at the point (3, ÷) is 2 A. x+16y+11= 0 B.…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: The function is given in parametric form by the equations{x=t2+t−1y=t3−2t.Find the second-order…

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Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: Find the derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…

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Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations…

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Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

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Q: Consider the smooth parametric curve defined by the equations = t (t² − 3) = 3 (t² − 3)' X Y where…

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Q: Given a surface f(x,y) = -3x + (4)y². Find the derivative in the direction of v = at the point (6,…

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Q: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: Include the plots of the solutions for y(x) and its derivative! d²y 34 + 2y = 0, initial condition:…

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Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6…

A: Differential equation

Q: Find the equation of the tangent line for f(x) = 6 tan(x) at a = %3D a) Oy = 6/3 (z -) + + 12 b) Oy…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Given a particle is moving in a curve r(t) = cos 7t i + sin 7t j + 6t k. Find the tangential…

A: Given a particle is moving in a curve rt=cos 7t i^+sin 7t j^+6t k^to find the tangential and normal…

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…

A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3   Apply the chain…

Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

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Q: (2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

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Q: A curve is defined implicitly by the equation x²+xy+y³=1 dy Differentiate implicitly to find dx

A: Follow the procedure given below.

Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

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Q: [&+2y)dx +(x² - 3y°)dy (3+2 4. Evaluate where C is any smooth curve from the point A (1, 0) to the…

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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.…

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

A: Use chain rule of differentiation to solve this problem.

Q: Find an equation of the tangent line to the curve a = t sin t, y = t cos t att = 5. Lütfen birini…

A: Given,  x= t sin(t)y=t cos(t) To find : The equation of a tangent line. Solution: The slope of…

Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

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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: 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: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha

A: The given problem is to find the nth derivative of y with respect to x of the given parametric…

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

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Q: VI. x = v1 - t , y = t³ – 3t

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