In numbers 5-7,
(a) make a table of values of t, x and y based on the specified intervals of the given parametic equations
(b) sketch the plane curve defined by the given parametic equations at the specified interval
(c) find dy/dx without eliminating the parameter t. simplify your answers
(d) find an equation such that the parameter t is eliminated
5. x=t²+1 and y=t³-2 for 0≤t≤2
6. x=sqrt(5t) and y=2t+2 for 0≤t≤5
7. x=cost and y=2-cos²t for 0≤t≤π
5.
(a)
(b)
(c)
(d)
"t=-\\sqrt{x-1}, t<0"
"y(x)= \\begin{cases}\n -(x-1)^{3\/2}-2 &t<0 \\\\\n (x-1)^{3\/2}-2 &t\\geq0 \n\\end{cases}"
6.
(a)
(b)
(c)
(d)
"y(x)=\\dfrac{2}{5}x^2+2, x\\geq0"
7.
(a)
(b)
(c)
(d)
"y(x)=2-x^2, -1\\leq x\\leq1"
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