. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t)...

. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t) = 5e^3t cos(4t) − 6e^2t sin(7t)

Expert Solution

Colby Messinger answered 1 year ago

1. Find the Laplace transform of each of the following functions: (a). f(t) = t ,...

1. Find the Laplace transform of each of the following functions: (a). f(t) = t , (b). f(t) = t2 , (c) f(t) = tn where n is a positive integer Laplace transform of the given function 2. . f(t) = sin bt 3. f(t) = eat sin bt

Find the Laplace Transform of the functions t , 0 ≤ t < 1 (a) f(x)...

Find the Laplace Transform of the functions t , 0 ≤ t < 1 (a) f(x) = 2 − t , 1 ≤ t < 2 0 , t ≥ 2 (b) f(t) = 12 + 2 cos(5t) + t cos(5t) (c) f(t) = t 2 e 2t + t 2 sin(2t)

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < ...

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < t ≤ 4 8 t ≥ 4 (b) f (t) = { t2 0 ≤ t < 3 0 t ≥ 3 (c) f (t) = { 0 0 ≤ t < π/4 cos[7(t − π/4)] t ≥ π/4

Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2...

Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2 sin^2(t) g(t)=3e^tcos(t)

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)=...

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)= 3) Find the Laplace transform of f(t)=u(t−6)⋅t^2 F(s)=

Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t), with initial condition y(0)=4, A)Find the Laplace transform of the solution...

Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t), with initial condition y(0)=4, A)Find the Laplace transform of the solution Y(s).Y(s). Write the solution as a single fraction in s. Y(s)= ______________ B) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form (c/(s-p)), where c is a constant and the root p is a constant. Both c and p may be complex. Y(s)= ____ + ______ +______ C)...

Find the Laplace transform of the following functions: a. p(t) = 6[u(t − 2) − u(t...

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Let g(t) = 5t − 3 ln(t 2 ) − 4(t − 2)2 , 0.1 ≤...

Let g(t) = 5t − 3 ln(t 2 ) − 4(t − 2)2 , 0.1 ≤ t ≤ 3. a. Find the absolute maximum and minimum of g(t). b. On what intervals is g(t) concave up? Concave down?

Find the Laplace transform of d2y/dt2

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t)...

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t) Find f'(4) 3.) Find the derivative of the function g(x)=(4x2+x−5)ex g'(x)= 4.) If f(x)=(5−x2) / (8+x2) find: f'(x)= 5.) If f(x)=(6x2+3x+4) / (√x) , . then: f'(x) = f'(1) = 6.) Find the derivative of the function g(x)=(ex) / (3+4x) g'(x)= 7.) Differentiate: y=(ln(x)) /( x6) (dy) / (dx) = 8.) Given that f(x)=x7h(x) h(−1)=2 h'(−1)=5 Calculate f'(−1) 9.) The dose-response for a specific...

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