Show that the curve given by, R(t)=(2sint)i+(2sint)j+(sqrt(8)cost)k lies on a sphere centered at the origin?

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

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Q: Evaluate fF dR given that F(x, y) = 2yî + (xy – 2x)j and C is the curve in the third quadrant from…

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Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

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A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find the equation of the tangent at the endpoints of the diameter - of circle (x − a)² + (y – b)² =…

A: Diameter makes an angle 6 with the x-axis.Therefore,Slope of diameter AB=tanθ∴Slope of tangents at A…

Q: 7 TT 4) Let cos 0 = - for <0 < . Find the exact value of: 25 2 a) sin soff CAH b) tan 0 xx

A: We know that sinθ is defined by the ratio PerpendicularHypotenuse, cosθ is defined by the ratio…

Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

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Q: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

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Q: What about the part where it has to be part of the curve r= sqrt(2cos(2theta))?

A: As per the question to evaluate the volume of a cylinder with specific geometric properties, we can…

Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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Q: 5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact…

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