Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: x² cos²y – sin y = 0, (0, ) re (a) tangent and (b) normal to the curve at the given

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

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Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

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: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Find the equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: What is the equation of the tangent plane to the surface y = eº cos (z) at the point (1, e, 0)?

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Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: Find an equation for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)

A: The given equation is z+1=xy2cosz. The objective is to find an equation for the tangent plane to the…

Q: Find an equation for the tangent plane to the surface z = 4xy® + sin(rx) at the point (1, 1, 4)

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Q: Determine the equation of the tangent plane to the surface z = cos(x + 2y) at the point (2,-1,0).

A: Tangent plane to f(x, y) at (x0, y0) is given by below:

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: Find an equation for the tangent plane to the surface 4xy6 + sin(rx) Z = at the point (1, 1, 4)

A: We have to find the tangent plane  of z=4xy^6+sin(πx) at (1,1,4)  Find the partial derivative with…

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y. (4, 0,…

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Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

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Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Consider the parametric curve C given by X= St. y = 5 sin²t where te [0.2] (₁) Determine the values…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which 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: Please solve

A: Parametrization of tangent lines is given by

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

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Q: Find the arc length of the parametric curve: x = e'(sint + cos t), y = e'(cost - sint) OstsIn3

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: Find the length of the parametric curve. X =t+ sint -T<t<π | ly=t2 + cost Set up the integral, then…

A: HEre we have to find the arc length of the given parametric curve

Q: Find the slope of the tangent line to polar curve r = 8 sin 0 at the point

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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: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

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 an (1,1) equation of the tangent i ine at the curue yt+xy = x_x+a. on

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Q: VI. x = v1 - t , y = t³ – 3t

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