An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.)
(a) The area of the right triangle is
a(t)= .
(b)
lim t → pi/2−a(t)=
(c)
lim t → 0+a(t)=
(d)
lim t → pi/4 a(t)=
(e) With our restriction on t, the smallest t so
that a(t)=2 is
(f) With our restriction on t, the largest t so
that a(t)=2 is
(g) The average rate of change of the area of the triangle on the
time interval [π/6,π/4] is .
(g) The average rate of change of the area of the triangle on the
time interval [π/4,π/3] is .
(h) Create a table of values to study the average rate of change of
the area of the triangle on the time intervals
[π/6,b], as b approaches π/6
from the right. The limiting value is .
(i) Create a table of values to study the average rate of change of
the area of the triangle on the time intervals
[a,π/3], as a approaches π/3
from the left. The limiting value is .
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < ?/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.)
I just need help with question F An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t), sin(t)). Assume 0 < t < pi/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.) The identity sin(2t)=2sin(t)cost(t) might be useful in some...
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
Activity: A Journey Through Calculus from A to Z sin(x-1) :- 1) x< h(x) kr2 - 8x + 6. 13x53 Ver-6 – x2 +5, x>3 Consider f'(x), the derivative of the continuous functionſ defined on the closed interval -6,7] except at x 5. A portion of f' is given in the graph above and consists of a semicircle and two line segments. The function (x) is a piecewise defined function given above where k is a constant The function g(x)...