Search & Filtering
Given equation, v(t) = 3 Cos(πt) − 2Sin(πt) (Eq. 1)
● v(t) is the instantaneous velocity of the car (m/s)
● t is the time in seconds
a)Find a mathematical model (e.g. equation) to correlate position and
time using an Excel sheet and trendline.
b)Find an accurate mathematical model (e.g. equation) to correlate
position and time. To complete this task you should be able to sketch
the graph again, find the accurate equation using an excel sheet and
trendline.
c)Compare the R2 between the new and previous equations (step a) and b) ).
d) Use the driven equation x(t) from (a) and solve it using the following
numerical methods over the time interval 0 ≤ t ≤ 3 seconds at h=0.5.
I. Using the trapezium method
II. Using a Simpsons rule
Given the equation,
v(t) = 3 Cos(πt) − 2Sin(πt) (Eq. 1)
● v(t) is the instantaneous velocity of the car (m/s)
● t is the time in seconds
Your tasks is
a) Derive an equation x(t) for the instantaneous position of the particle as
a function of time using indefinite integration.
b) Sketch a graph of position vs. time over the time interval 0 ≤ t ≤ 3
seconds for Eq.1, where C=12.
c) Find a mathematical model (e.g. equation) to correlate position and
time using an Excel sheet and trendline.
d) Using definite integration and driven equation (from c) to find the
position over the time interval 0 ≤ t ≤ 3 seconds and C=12.
e) Using a mid-ordinate rule and driven equation (from c) to find the
position over the time interval 0 ≤ t ≤ 3 seconds at h= 0.5.
f)Find an accurate mathematical model (e.g. equation) to correlate
position and time. To complete this task you should be able to sketch
the graph again, find the accurate equation using an excel sheet and
trendline.
Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x 2 2 , ∀ x > 0
Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x 2 2 , ∀ x > 0
The region bounded by y = 3-e^-x, the x-axis, x =2 and the y-axis
lim (x.cosx- sinx / x^2.sinx)
x→0
Find the second Taylor polynomial of
f(x,y) = xy+3y^2-2 at (1,2)
Verify Euler's realtion for
z= tan(y/x) ,x ≠ 0
Let the function,f be defined by
f(x,y) = { 3x^2y^4/(x^4+y^4) , (x,y)≠(0,0)
{ 0 ,(x,y)={0,0)
Show that f has directional derivatives in all directions at (0,0).
Hands-On Calendar has found that the cost per card of producing x pocket calendar cards is given by
C'(x) = -0.02x + 50, for x ≤ 800,
where c(x) is the cost, in cents, per card. Find the total cost, in dollars, of producing 550 cards.
