Homework Answers
In the given integral, the function other than sine function is
known as dirac-delta function. The dirac delta function has only
one value that is at t=0 for 
. The given dirac-delta function is 
it means that the function has the value at t=3.
Now coming to the integral the solution to this type of integral is the value of the function other than dirac-delta at t=3 because the integral of the dirac-delta function over the time-period 0 to 7 is 1 as the time-interval includes the value of dirac-delta with in its range.
If the dirac-delta function is only
then the value of integral is given by the value of the function
other than dirac-delta at t=0.
If the interval of the integral doesn't have the dirac-delta function within it, its integral value will be value of the function other than delta-dirac at t=0.
So the value of the integral of the given function is Sin(pi*t/3) at t=3 which is Sin(pi*3/3).
Therefore, the value of integral = Sin(pi) = 0
Therefore, the answer for the given problem is Option A.
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use...
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t 1. For a tolerance of e-0.01, use a based on absolute error stopping procedure
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t...
(2) Apply Cauchy's Integration to EVALUATE the following INTEGRAL: 27 1 dt. 0 3 – sin(t)
(2) Apply Cauchy's Integration to EVALUATE the following INTEGRAL: 27 1 dt. 0 3 – sin(t)
3. Evaluate: The value f(4) for the continuous function f satisfying 2 sin = f(t) dt
3. Evaluate: The value f(4) for the continuous function f satisfying 2 sin = f(t) dt
g(0) is defined below, g(t) 3 3 k (1) Write the mathematical expression as a series...
g(0) is defined below, g(t) 3 3 k (1) Write the mathematical expression as a series chose at least the five samples showin (2) Express your answer in a summation format Useful Identities L[x(t))x(t)e-st dt 0 jot j0t at cos 2θ (s+ α)2 y (t) = x(t) * h(t) = | x(t)h(t-t) dr
Using matlab solve numerically dy/dt = sin t, y(0)=0 for 0<=t<=4π the exact solution is y(t...
using matlab solve numerically dy/dt = sin t, y(0)=0 for 0<=t<=4π the exact solution is y(t) = 1 - cos t. Compare the exact and numerical solution.
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t)...
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t) dt. Evaluate the following limit. 2022
st sin t dt = -(A) - tan s (B) tan1s tan-ls (C) tan-1s (D) T-...
st sin t dt = -(A) - tan s (B) tan1s tan-ls (C) tan-1s (D) T- (E) None
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) li...
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
Consider the following initial value problem dy dt = (1 – t)y + sin y with...
Consider the following initial value problem dy dt = (1 – t)y + sin y with y(-1) = 0.5 We want to find y(2) with an absolute error below 10-8.
Q2 Given that: T/2 di, T/2 | -T/2 T/2 a" = f (t)cos dt and -...
Q2 Given that: T/2 di, T/2 | -T/2 T/2 a" = f (t)cos dt and - sin T/2 for n = 1, 2 , determine the Fourier Series for f(t), where: f(t) = 1, for-1 t <-, f(t) = 0, for _ < t ST and f(t +2n) = f(t). Write down the first five non-zero terms in the series.
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t 1. For a tolerance of e-0.01, use a based on absolute error stopping procedure
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t...
(2) Apply Cauchy's Integration to EVALUATE the following INTEGRAL: 27 1 dt. 0 3 – sin(t)
3. Evaluate: The value f(4) for the continuous function f satisfying 2 sin = f(t) dt
g(0) is defined below, g(t) 3 3 k (1) Write the mathematical expression as a series chose at least the five samples showin (2) Express your answer in a summation format Useful Identities L[x(t))x(t)e-st dt 0 jot j0t at cos 2θ (s+ α)2 y (t) = x(t) * h(t) = | x(t)h(t-t) dr
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t) dt. Evaluate the following limit. 2022
st sin t dt = -(A) - tan s (B) tan1s tan-ls (C) tan-1s (D) T- (E) None
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
Consider the following initial value problem dy dt = (1 – t)y + sin y with y(-1) = 0.5 We want to find y(2) with an absolute error below 10-8.
Q2 Given that: T/2 di, T/2 | -T/2 T/2 a" = f (t)cos dt and - sin T/2 for n = 1, 2 , determine the Fourier Series for f(t), where: f(t) = 1, for-1 t <-, f(t) = 0, for _ < t ST and f(t +2n) = f(t). Write down the first five non-zero terms in the series.
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