Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² = 25 and y² +z? = 25

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: 2∂z∂x=2xaa=xp, where p=∂z∂x2∂z∂y=2ybb=yq, where q=∂z∂y2z=x2xp+y2yq2z=px+qy

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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

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Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

A: The slope of the tangent is:

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the derivative of the following parametric equation. x = 2 sece y = 3tan0 at 0 %3D 6

A: Here we will find derivative of given parmetric equation,

Q: x=e"Cost = e"S int

A: Given: x=e-tcosty=e-tsint At t=0: x=1, y=0 Differentiating both with respect to t:…

Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

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

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Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

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Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 - 4t +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…

A: we want to find the tangent lines to theparametric equations given byx=f(t)  y=g(t)The equation of…

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the equation of the tangent plane to the surface 3 – 12y – sin(r*:) = 0 at the point (2, 1,0).…

A: To find gradient of the function.

Q: Find the equation of tangent line of curve That is given by parametric equations x=3cost+sint y=e2t

A: The equations are x=3cost+sint,y=e2t The derivatives w. r. t t are given by:…

Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

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

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Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Find the equation – in any convenient form – of the tangent plane to z = x² sin(x+2y) at the point…

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Q: Find the equation of the tangent line to the curve with parametric equations x=cost, y=sint at…

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Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²) + 1 at (x,y)= (…

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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: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

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Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview

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Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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Q: Find the derivative of the parametric curve x=2+cost, y=1+sint at the point t=π3.

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y > 0, using as parameter the slope t…

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Q: Find the second derivative of the parametric equation = 9t2 + 4 , y=3(t − 2)2

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Q: a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint…

A: The slope of the tangent at a point on the curve, y=f(x) is equal to the first derivative of the…

Q: u =1-1,y=6-2+름 x = 1-, y = 6-

A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…

Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

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Q: Find the tangent plane to the equation 3y cos(5x – 4y) at the point (4,5,15)

A: z=3y cos5x-4y Let, Fx,y,z=3y cos5x-4y-z=0  ......(1) Now,  Fx=∂Fx,y,z∂x=-3y sin5x-4yx5-0…

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: Find the equations of the lines tangent and normal to the curve guen by para- metric equations at +…

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Q: Find the exact length of the curve. y = In(sec(x)), 0≤x≤ w|ले

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