y = In(sec t), x = log(cosec t) In(sect), x %3D %3D

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: (х+ siny)dx+ (хcosy— 2y)dy 3D0

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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 a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Compute the surface area of the surface generated by revolving the astroid with parametrization c(t)…

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Q: Find the slope of the tangent line to the parametric curve [x = 4 cos(t) y = 3 sin(t) at the point

A: A detailed solution is given below.

Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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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: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

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Q: et secydx + sinydy = 0

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Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

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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 a curve through the origin in the xy- plane whose length is given by 1/2 L = [; (1+ *)"* dx 4

A: The arc length, L of a curve y=f(x) in the interval a,b is calculated using the formula below.…

Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

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 the derivative dydx of Fermat’s spiral given by the polar equation r=√θ.

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Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

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Q: Integrate by changing to polar coordinates. '3 8x dx dy

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find dy/dx in terms of x and y if arcsin(x'y) = xy". dy dx Submit

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: A thin plate part with a mass density equal to 1 and shape as shown in Figure 2 has an edge curve C…

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Q: Determine the singular points of (x−π2)2y′′+(cosx)y′+(sinx)y=0 and classify them as regular or…

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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: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: The plane tangent to the surface z+1= ze" cos z at (1,0,0) can be represented by the equation Z= 1.…

A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…

Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: Describe the motion of a particle with posi- tion P(x, y) when x = 5 sin t, Y = 2 cost

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Q: Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant…

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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: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: 2dy -2y 2. zt at

A: Solved below

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: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: if t(い) = ta Cosy V = X siny Determine JR ļ JR to つメ

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Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Find dz/dy of z=arctan (x/y)

A: The given function is z=tan-1xy.

Q: what  is the arc length of the parametric curve x=cos2 θ y=cosθ and  θ  is bounded between 0 and π/2

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Q: Let C be the curve which uses straight line segments to travel from (0, 0) to (0,1) to (2,0) and…

A: The curve C is the line segments travels from 0, 0 to 0, 1 to 2, 0 and then back to 0, 0. Draw the…

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³ = 4x²y³ Determine dy/dx…

A: See this solution in below

Q: dy Use implicit differentiation to find dx X+3 %3D У -3 3y = dy %3D dx

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Q: Find the derivative dydx of the polar function r=sec(2θ) at θ=π4

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Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…