009C Sample Final 3, Problem 10

A curve is described parametrically by

$x=t^{2}$

$y=t^{3}-t$

a) Sketch the curve for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2\le t \le 2.}

b) Find the equation of the tangent line to the curve at the origin.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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