On a separate sheet of paper sketch the parameterized curve

On a separate sheet of paper, sketch the parameterized curve x=tcost y=tsint for 0<=t<=4pi. Use your graph to complete the following statement:

At t=3.5, a particle moving along the curve in the direction of increasing t is moving down and to the right.

(b) By calculating the position at t=3.5 and t=3.51, estimate the speed at t=3.5.

speed __________?

(c) Use derivatives to calculate the speed at t=3.5 and compare your answer to part (b).
speed = __________?

Solution

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On a separate sheet of paper, sketch the parameterized curve x=tcost y=tsint for 0<=t<=4pi. Use your graph to complete the following statement: At t=3.5,

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