Question

3. Let C be the curve parametrised by r(t) = (cost, sint - 1,2 - 2 sint), where 0 ? t ? 2?. (a) Find three different surfaces on which C lies. (b) Sketch the curve C. (c) Find a vector equation for the line tangent to C at the point P(1, -1,2). (d) Find the curvature of C at the point P. (e) Find a Cartesian equation for the osculating plane to C at the point P.

          3. Let C be the curve parametrised by r(t) = (cost, sint - 1,2 - 2 sint), where 0 ? t ? 2?.
(a) Find three different surfaces on which C lies.
(b) Sketch the curve C.
(c) Find a vector equation for the line tangent to C at the point P(1, -1,2).
(d) Find the curvature of C at the point P.
(e) Find a Cartesian equation for the osculating plane to C at the point P.

3. Let C be the curve parametrised by r(t) = (cost, sint - 1,2 - 2 sint), where 0 ? t ? 2?.
(a) Find three different surfaces on which C lies.
(b) Sketch the curve C.
(c) Find a vector equation for the line tangent to C at the point P(1, -1,2).
(d) Find the curvature of C at the point P.
(e) Find a Cartesian equation for the osculating plane to C at the point P.

Added by William B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

04/17/2023

Step 1

To find surfaces on which C lies, we can look at the components of the parametric equation r(t). Show more…

Show all steps

Thanks for your feedback!

Let C be the curve parametrised by r(t)=(cost,sint-1,2-2sint), where 0<=t<=2pi . (a) Find three different surfaces on which C lies. (b) Sketch the curve C. (c) Find a vector equation for the line tangent to C at the point P(1,-1,2). (d) Find the curvature of C at the point P. (e) Find a Cartesian equation for the osculating plane to C at the point P. 3. Let C be the curve parametrised by r(t) = (cos t, sin t -- 1, 2 -- 2 sin t) , where 0 t 2t. (a) Find three different surfaces on which C lies. (b) Sketch the curve C. (c) Find a vector equation for the line tangent to C at the point P(1, --1, 2) (d) Find the curvature of C at the point P. (e) Find a Cartesian equation for the osculating plane to C at the point P.