Exercises 9.1

Excesses 4-6. Sketch the plane curve defined by the given parametric equations and find an x-y equation for the curve.

Q4) [x=4+3t, y=2-4t

Q6) {x=2-t, y=t²+1

Q24) . Find parametric equations describing the given curve

(a)The line segment from (4, -2) to (2, -1)

b26. The portion of the parabola y=2- from (2, -2) to (0, 2)

Exercises 9.2

Exercises 2-10, find the slopes of the tangent lines to the given curves at the indicated points.

(2) { x=t³ -t, y=t⁴-5t²+4, (a) t= -1, (b) t=1, (c) {0, 4}

(4) {x=cos 2t & y=sin 4t (a) t=pi/4 (b) t=pi/2 and

(c) { square root 2/2, 1}

Exercises 9.3

In exercises 1-8, find the arc length of each curve; compute one exactly and approximate the other numerically.

2a) {x=t³-4, y=t²-3, -2 less than equal to t less than equal 2

2b) x=t³-4t, y=t²-3t, -2 less than equal t less than equal 2

6.a) { x=sin t, y=pi sin t, 0 less than equal t less than equal pi

6.b) { x=sin t, y=pi sin t, 0 less than equal t less than equal pi

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