Produce three isoclines with appropriate direction markers, and sketch one solution curve passing through x = 2 for the equation dy = 2x. dx %3D

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: H.w Find the enlsed between yasinx, ya cas X arca

A: In the question it is asked to calculate the are enclosed between y = sin(x) and y = cos(x) when x…

Q: he unit circle x^2 + y^2=1 can be written in parametric form  as x=cos(θ) and y=sinθ. Find dy/dx…

A: The parametric equation of the unit circle is: x=cosθ ; y=cosθ From the chain rule we know that,…

Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

A: We are given the parametric equations: x=6cosθy=6sinθ We know that the derivative of  cosa=-sina and…

Q: Eliminate the parameter to find the Cartesian format, then sketch the graph: а. x = cost y = cos² t…

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Q: Find the arc length of the graph of the given equation from A to y = 6x2/3 + 1 А(-1,7), В(—8,25) B.

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

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Q: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the arc length of the asteroid x2/3 + y2/3 = 32/3.

A: Given curve is

Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: Find a cosine equation of the given sinusoidal function. JY

A: we have to find out cosine equation of given sinusoidal function

Q: equation

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

A: Given: The parametric equation are: x=6cosθ        ... (1)y=6sinθ         ... (2)

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: Find the exact length of the curve r = sin 0 + cos 0.

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Q: Find the arc length of the asteroid x2/3+y2/3=72/3

A: We have given; x2/3+y2/3=72/3

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

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: Use the Quadrature Rule Calculate I = S e2x dx using the 3-point Gaussian Quadrature method.

A: Given integral is I=∫03e2xdx

Q: 11. dy/dx = -x/y, y(0) = 4 %3D

A: Given: Let's sketch the isoclines and their direction markers, then sketch a few solution curves,…

Q: The derivative I of the parametric equations and y=5vt is

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Q: Find the arc length of the graph of the given equation from A to B (x+3)2 = 8 (y-1)3 A(-2,3/2)…

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Q: If X =r cose equation (d ,y=r sin@ then show that the will be Erans formed into dy 2. 3D0 dr

A: Change of Variables: Suppose where and Then and

Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0<=t<=pi Arc…

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: stuck on the attached problem

A: Please refer to the white board. We have to find the volume shaded in the first diagram. This volume…

Q: b) flx)= + Arcsin lenx) ,Dp=! %3D Jex+1|-3

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

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Q: Find the length of the curve r = 4 – 4 sin 0

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Q: It takes jupiter 11.64 yr to complete one circular orbit around the sun. If jupiter's avarage…

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Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: The value of [xe*dx by using the three-segment trapezoidal rule is most nearly

A: by trapezoidal rule

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

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Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

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Q: 2. Find the SA generated by rotating the first quadrant portion of the curve y = 9- x2 about the…

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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: ) Find the arc baynded by yr-x? +1; y:-2xt2, X--2 and y 2.

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Q: Find dy/dx in terms of a and y if arcsin(x'y) = xy". dy da %3D

A: Consider: sin-1x7y=xy7. Calculate dydx.   Derivate both side with respect x and apply chain rule.…

Q: 2 [arc cos ( Incs-2) fdz ( Incs-z>) ] dz

A: