#$&*
course Mth 173
10/7/2012
Query 3Question 1-Query Class notes #04 explain how we can prove that the rate of depth change function for depth function=t^2+bt+c is y=2at+b
My solution-the average rate is between the clock times t and t+dt. [ a (t+`dt)^2 + b (t+`dt) + c - ( a t^2 + b t + c ) ] / `dt = [ a t^2 + 2 a t `dt + a `dt^2 + b t + b `dt + c - ( a t^2 + b t + c ) ] / `dt= [ 2 a t `dt + a `dt^2 + b `dt ] / `dt= 2 a t + b t + a `dt.
@&
x^2 means x squared. You probably meant x_2 or x2, either of which could represent x with subscript 2.
In this case the independent variable is t, so the expression would be
(y2 - y1) / (t2 - t1).
For the specified function we have
t1 = t
t2 = t + `dt
so that
y2 = a (t+`dt)^2 + b (t+`dt) + c
and
y1 = ( a t^2 + b t + c )
t2 - t1 = (t + `dt) - t = `dt
so your expression
[ a (t+`dt)^2 + b (t+`dt) + c - ( a t^2 + b t + c ) ] / `dt
does constitute (y2 - y1) / (t2 - t1).
The term b t does not appear in the final expression. b `dt in the numerator is divided by the `dt in the denominator, leaving just plain old b.
You left off the part about the limit. As `dt approaches zero, 2 a t + b + a `dt approaches just 2 a t + b.
*@
Confidence-2
Self-Rating-2 Critique-I was a little confuse with determine the average I thought we do the y2-y1/x^2-x^1
Question 2-explain how we know that the depth function for rate of depth change function y=mt+b must be y=1/2 m t^2+bt+c for some constant c and explain the significance of the constant c.
My solution-Since 2at+b is all possible values of the parameter it is aso the same in both equation which the coefficient must be equal.C is constant because it depends only on when we start our clock and the position form which the depth is being measured
Confidence-2
Self-Rating-2
Self-Critique -I felt this particular problem wasn’t that hard
Question 3-Explain why given only the rate of depth change function y and time interval we can determine only the change in depth and not the actual depth at any time wheras if we know the depth function y we can determine the rate of depth change function
My solution-To get the answer you would have to multiply the average rate by the interval from the change in depth .so we all know the rate function we have no way to find the actual depth at any clock time
Confidence-2
Self-Rating-2
Self Critique-Why is the rate changing in the interval
@&
If the rate is changing, then we expect it to change on most intervals.
We would then need to start by finding or approximating the average rate for the given interval.
*@
Question 4
In terms of the depth model explain the processes of differentiation and integration
My Solution-Rate of depth change from the depth data, which makes it a differentiation. Given rate of change information it is possible to find change but not the depth
"
&#Your work looks good. See my notes. Let me know if you have any questions. &#