The equation z^2+y^2+x^2 = 4, represents the surface of a sphere. Using implicit differentiation, calculate ∂y/∂x(deltay/deltax) at the point [7,3,−3].

Q: b) For the curve 2² - 4ry² = y³ +9, do the following:

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Q: Let r be a positive real number. The equation for a circle of radius r whose center is the origin is…

A: Given equation: x2+y2=r2                     . . . (1) (a) Differentiating (1) with respect to x,…

Q: FIND THE SOPE OF THE TANGENT LINE TO 5x) AT THE POINT (x, 9(x)). 2.

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Q: Find the points on the ellipse                  x^2/a^2+y^2/b^2=1 such that the tangent at each…

A: The equation of the ellipse is x2a2+y2b2=1

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: What are tangential components?

A: Consider the provided information, What are tangential components.

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: of AB

A: Given curve Lets first find the tangent at (-2,4)

Q: Find the parametric equation to describe the following curve: b) the part of x = 2y^2 - 1 from…

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Q: fox)%= draw its cuve of function. by examíning the change sinx Secon

A: When the denominator is 0, the value of function approaches to infinity. Therefore, for the very low…

Q: Find the gradient of the function whose center is at the origin and radius of 7units…

A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…

Q: Trace the curve: r^2 = 4cos^4ꝋ tan^2ꝋ

A: The equation given in the question be, r2=4cos4θtan2θ Take square root on both sides implies,…

Q: d?y - =6-9x dx 2 Find the equation of the curve for which and which passes through the points (0,…

A: To find the curve satisfying the conditions

Q: 24=y cotx

A: Given differential equation is 2y'=ycotx.......1. We have to find the general solution of the given…

Q: Sketch a graph of the parametric curve defined by:  x = t^2 and y = t^3 - 4t  for − 2 ≤ t ≤ 2.…

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Q: Construct two different parameterizations of curves which connect (0, 1) and (1,0).

A: The objective of this question is to find two different parameterizations of curves that connect the…

Q: Calculate only the (complete) extensions of the curve: x^2 y + 2xy - x^2 + y = 0.

A: We have given the curve:The complete extension of the curve is the set of all points  that satisfy…