1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T :...
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?
For some positive integers t, y + 5 = (1/t) * (x^2) intersects
x^2 + y^2...
For some positive integers t, y + 5 = (1/t) * (x^2) intersects
x^2 + y^2 = 25 at exactly 3 points P, Q, and R (distinct from one
another). Determine the positive integers t for which the area of
triangle PQR is an integer.
Determine the interval(s) where r(t)=<
t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous.
And
Both r1(t)...
Determine the interval(s) where r(t)=<
t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous.
And
Both r1(t) = < t2,
t4 > and r2(t)
= < t4, t8 > map out the same half
parabolic graph.
Notice that both r1(1) = < 1, 1
> and r2(1) = < 1, 1
>.
However, r'1(1) = < 2, 4 >
and r'2(1) = < 4, 8
>.
Explain why the difference is logical and quantify the
difference at t=1.
Determine the interval(s) where r(t)=<t −...
7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3...
7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3
sin(t), t ∈ [0, 2π) Part a: (2 points) Give an equation relating x
and y that represents the curve. Part b: (4 points) Find the slope
of the tangent line to the curve when t = π 6 . Part c: (4 points)
State the points (x, y) where the tangent line is horizontal