Let C be the curve described by the parametric equations

prelimaf1 2021-12-04 Answered
Let C be the curve described by the parametric equations x(t)=t,y(t)=t3.
a) sketch a graph of C.
b) find the vector-valued function f(t) associated with this parameterization of the curve C.
c) find the velocity vector and the speed of f(t) at t=1.
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Expert Answer

kayleeveez7
Answered 2021-12-05 Author has 10 answers

Step 1
Given equation is
x(t)=t,y(t)=t3
Step2
To sketch the curve let convert it into Cartesian form
Put t=x in y=t3
y=x3
Step3
Graph of curve Cis as shown
image
Step4
b)
vector-valued function f(t) associated with this parameterization of the curve C.
f(t)=t3
Step5
c) the velocity vector and the speed of f(t) at t=1.
f(t)=3t2
Put t=1
f(t)=3t2
f(t)=3×12
f(t)=3

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