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11 Jun 2020

Using Functions

Consider the functions

and

(a) Find a set of parametric equations of the tangent line to the curve of intersection of the point and find the angle between the gradients of and .

(b) Use a computer algebra system to graph the surface and the tangent line found in part (a).

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Rico Jay Laxa
Rico Jay LaxaLv10
28 Aug 2020

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Related questions

Investigation

Consider the function

on the intervals and .

(a) Find a set of parametric equations of the normal line and an equation of the tangent plane to the surface at the point .

(b) Repeat part (a) for the point .

(c) Use a computer algebra system to graph the surface, the normal lines, and the tangent planes found in parts (a) and (b).

Investigation

Consider the function

on the intervals and .

(a) Find a set of parametric equations of the normal line and an equation of the tangent plane to the surface at the point .

(b) Repeat part (a) for the point .

(c) Use a computer algebra system to graph the surface, the normal lines, and the tangent planes found in parts (a) and (b).

Using Functions

Ā 

Consider the functions

and

(a) Use a computer algebra system to graph the first-octant portion of the surface represented by and .

(b) Find one first-octant point on the curve of intersection and show that the surfaces are orthogonal at this point.

(c) These surfaces are orthogonal along the curve of intersection. Does part (b) prove this fact? Explain.

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