Find the Laplace transform of the given function: f(1) = (1-6)u4 (1) - (1-4)u6 (1), where u. (t) denotes the Heaviside function, which is 0 for t

Q: Find the Laplace transform for :  f(t)= (t+3) H (t-4)

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Q: Find the Laplace transform for 1) (a) f(t) = t cosh 2t. (b) f(t) = e-4 cos 2t.

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Q: Find the inverse Laplace transform of F(x) = 4s^2−2s+2/(s2−4)(s)

A: The inverse laplace transform of F(s)=4s2-2s+2s(s2-4)

Q: Find the inverse Laplace transform of 1 F(x) S- s2 (s + 1)

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s).…

Q: determine the Laplace transform of the given function.

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Q: Find the Laplace Transform of f(t) = t² when t > 0.

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Q: Find the Laplace transform of: f (t) = t3 – 8t2 + 1 -

A: Topic  = Laplace transform

Q: determine the inverse Laplace transform of F.

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Q: f(t)=(3t + 4)(t² - 1)

A: Using standard formula & rules of Laplace transform.

Q: find the Inverse LaPlace Transform, L-1{F(s)}. L~1 s2 А. (t - 1)*и(t — 1) В. t u(t - 1) C(t – 2)U(t…

A: Given, L-1{e-s/s²} We know that, L-1(e-s)= theta(t-1) L-1(1/s²)= t

Q: Determine the Laplace Transform of the given function 1-t, 0<t<1 1-1, 1. f(t) = [0, 1st

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the inverse Laplace Transform of F(s) 2s2 + s -3 F(s) = s4 +3s2 + 2

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Q: find the Laplace transform by the method of the unit step function

A: The Laplace transform of the function f(t) is given by,

Q: Find the Laplace Transform of f(t) = 3e + 4t² - 2

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Q: Find the Laplace Transform of the Heaviside Function. f (t) = { -; for 02 3e 2 3e 24 3e 25

A: We have to find the Laplace transformation of given heaviside function.

Q: Find the Laplace transform, F(s), of this function f(t) = e-2t t cos 3t

A: We use first shifting Theorem to find the Laplace transform of given function which states that  IF…

Q: The Inverse Laplace Transform for 1/S-3 is u(t)e^3t e^-at t^2 t

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Q: The Laplace transform of f(t) - t U(t - 3) is:

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Q: Find the Laplace transform of the given function: f() — (t — 4)из() — (t — 3)и4(t), - where u.(t)…

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Q: F(s) s2 s-2 3. 5.

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Q: /Find the Laplace Transform -3 4- f(t) = v2 t re) () = Where r

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Q: Find the Laplace transform of the function: 0, 12 - 10t + 26, t>5 t < 5 f(t) = 2 L(s) = e-5s ° z0) =…

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Q: Obtain the Laplace transform of Ost 0.

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Q: d.-tte-6c 3

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Q: Find the Laplace transform of (t2 + 1)2.

A: we use the formula £(t^n)=n!/Sn+1. See 2nd step.

Q: Find the Laplace transform of f (t) = {5-1 O2 s2 e-2s s2

A: This question based on Laplace Transformation.

Q: find the Laplace transform by the method of the unit step function

A: Consider the provided function:

Q: find the Laplace transform by the method of the unit step function

A: The given function,

Q: Find the Laplace transform of: 1. f(t) = e(3t-7) cos³ (6t)

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Q: What is the Laplace transform of the function f(t)=(2t−1)³?

A: We have to find the Laplace transform of the function f(t)=(2t−1)3.

Q: Find the Laplace transform of: 1. f(t) = e(3t-7) cos³(6t) %3|

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the Laplace transform of f(t) = (t² + 1)²

A: Use Laplace table.

Q: The Laplace transform of f (t) 0 <t< 2 is: t2 2

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Q: Find the Laplace transform of the following function f(t) = u(t-5)e-) cos 5t

A: First we will use the property of Laplace transform.

Q: Find the inverse Laplace transform of: - s-3 i) F(s) = %3D (s-3)2+4 s-2

A: It is known that:

Q: determine the inverse Laplace transform of the given function.

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Q: Find the Laplace transform, F(s) of the function f(t) = – 9t* – 7 cos(2t), t> 0 - F(s) = ,8 > 0

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Q: Find the Laplace transform of L{t^2cost}

A: Laplace transform of the form L(tkf(t))=(-1)kdkdskLf(t) Here, k=2, f(t)=cost From the identity,…

Q: The Laplace transform of f (t) = {", 0<t< 2 is: t2 2

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Q: Find the Laplace transform of f(t) = 31° - 8 cos 4t + e-24.

A: We will use the Laplace transform formulae to find the Laplace transform of the function f(t)

Q: F(t) = 2T, 0 < t <3; F(t+ 3)u(t – -

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Q: f(t)=(e^−4t−e^−t)^2

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Q: Find the Laplace transform of the given function: f(t) = (t – 7)u3(t) – (t – 3)u7(t), - where uc(t)…

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Q: Find the Laplace transform for e¹t (t² + 3t+5)

A: Given function is e4tt2+3t+5. To find: Laplace transform of the given function. Formula used: If…

Q: Find the Laplace Transform of the following functions 2(1-e **) -TS 11) 2 Ans. F(s)= S t

A: As we know that the Laplace transform for a function f(t) is :- Lf(t=∫-∞∞f(t)e-stdt

Q: Obtain the Laplace transform of t2 + 4t - 5.

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Q: Find the Laplace transform of the given function: f(t) = (t – 4)u2(t) – (t – 2)u,(t), where uct)…

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Q: Find the Laplace Transform of f -1 Osx<1 f(x) = 1 x21 2e-s 1 a. 2e-s 52 1 b. 2e-s 1 C. 2e-s 1 d. +

A: We find Laplace transform of given function

Q: b) f(t) = t*e3t

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Q: Find the inverse Laplace transform of 2s+1 a) F(s) = s²+25 7 b) F(s) s(s-3)

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.