1) You know that y\'[x] = a y[x] for all x \'s but DO NOT know the value of a .
ID: 2879268 • Letter: 1
Question
1) You know that y'[x] = a y[x] for all x 's but DO NOT know the value of a . How many data points of the form {x, y[x]} do you need to determine a formula for y[x] ?
2) You know that y'[x] = a y[x] for all x 's and you DO know the value of a . How many data points of the form {x, y[x]} do you need to determine a formula for y[x] ?
3) You know that y'[x] = a y[x] for all x 's and you know that a is positive and that y[x] is always positive. Does y[x] go up or down as x advances from left to right?
4) Pencil in a rough sketch of the solution of
y'[x] = 0.2 y[x] with y[0] = 1
on the axes below.
5) You know that y'[x] = a y[x] for all x 's and you know that a is negative but that y[x] is always positive. Does y[x] go up or down as x advances from left to right?
6) Pencil in a rough sketch of the solution of
y'[x] = -0.5 y[x] with y[0] = 6
on the axes below.
7) You know that y'[x] = a y[x] for all x 's and you know thaty[0] = 5 . Can y[x] ever go negative? Why?
8)Is there any x that makes e^x negative?
9)You know that y'[x] = a y[x] for all x 's and you know that a is positive. What is the value of
[lim, x Infinity] y[x]/x^10 ?
10) You know that y'[x] = a y[x] for all x 's and you know that a is negative. What is the value of
[lim, x Infinity] y[x]/x^10 ?
11) You know that y'[x] = a y[x] for all x 's and you know that y[x] is positive for all x 's. How does the Log[y[x]] curve plot out?
Explanation / Answer
1) Two data points needed
2) One data point needed
3) As we know that a is positive and that y[x] is always positive, thus y'[x] is always positive and hence y[x] increases so it goes upwards as x moves from left to right
4)
5) As we know that a is negative and that y[x] is always positive, thus y'[x] is always negative and hence y[x] decreases so it goes downwards as x moves from left to right
8) No
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