2. Solve dy dt =-y+28(t-3), y(0) = 1.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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Solve q 2 please
![Note: Recall that the delta function 8(t) is the first derivative of the step function H(t). The
key property of 8(t) is the way it behaves in integrals: for any number c and any function f,
S..
[f(c), a<c<b,
f(s)8(sc) ds =
0,
otherwise,
i.e. the integral "picks out" the value of the function f at the location c where 8(t-c) has a
spike. The integral is zero if the spike lies outside the domain of integration.
For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step
function:
1. Evaluate the following integrals involving (t):
[.. es cos(s) (s-2) ds.
(a)
(b)
S
[ f(s)8(s — c) ds = f(c)H(t - c).
2. Solve
(8³+ s)8(s-2) ds.
(c)
S s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.)
=-y+28(t-3), y(0) = 1.
dy
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc904c82f-560b-4ff5-bc55-8616059f1008%2Fc26f0766-bc03-4c0d-8c68-4b87922221d7%2F9ehvqe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Note: Recall that the delta function 8(t) is the first derivative of the step function H(t). The
key property of 8(t) is the way it behaves in integrals: for any number c and any function f,
S..
[f(c), a<c<b,
f(s)8(sc) ds =
0,
otherwise,
i.e. the integral "picks out" the value of the function f at the location c where 8(t-c) has a
spike. The integral is zero if the spike lies outside the domain of integration.
For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step
function:
1. Evaluate the following integrals involving (t):
[.. es cos(s) (s-2) ds.
(a)
(b)
S
[ f(s)8(s — c) ds = f(c)H(t - c).
2. Solve
(8³+ s)8(s-2) ds.
(c)
S s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.)
=-y+28(t-3), y(0) = 1.
dy
dt
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