Q1) Given f (t) = t* + 3t2 + 7t+1, determine whether or not initial conditions are required for the simplification of the following operations: y(t) = D*f (t).

Q: (b) Find f-¹(y) for f(x) = √²-1.

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Q: Let f(x) = 5x² - 4 to find the following value. f(t+1) f(t+1)= 5t+10t+1

A: Given f(x)= 5x2-4

Q: how did you determine your t values for the piecewise function?

A: Given that yc=0t≤0ce-1tt>0 Here "y" is a Piecewise function.

Q: When f(x) = 8a? – x – 3, evaluate f( – 4) f( – 4) =

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Q: f (x) = Vx² – 4.

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Q: 8 Use definition L{f(t)} = - S% e- 0 -st f(t) dt to find L{3t}

A: From definition of Laplace integral  for function ,, Here

Q: Find the function value, if possible:q(t) = (2t2 + 3)/t2 (a) q(2) (b) q(0) (c) q(−x)

A: We have to find the function value: a  q2b  q0c  q-x For the given function: qt=2t2+3t2 In this case…

Q: dy Q1: - Find of the following functions dx x2 +3 b. y = (x-1)3+(x+1)3

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Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: During the first 12 hour, the employees of a machine shop prepare the work area for the day’s work.…

A: The machine parts is a function of time ft=10t-12 Cost of producing machine parts Cx=.1x2+25x+200,…

Q: 2) Differentiate and simplify: f(t) = 2et e2t+ 1

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Q: Find all the inflection points of f(x) = x4 – 2x3 – 12 – 5x2 - - -

A: The given function f(x)=x4-2x3-12-5x2

Q: Find the point of f(x) = 2x3 - 9x2-17x - 3 is at [0, 00) on which concavity changes. %3D

A: We draw graph of given function.

Q: Put the function Q= (t-2)(t+2) - (t+4)(t-1) in the form Q= it and state the value of k

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Q: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

A: Given that x=(1,1) and y=(5,-1)

Q: A radioactive substance has a half-life of one week. In other words, at the end of every week the…

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Q: Find the number of zeros of g(2) = z+z++2:²+1 in the first quadrant,where z €

A: Given function is gz=z13+z4+2z2+1. We have to find the number of zeroes of gz in the first quadrant…

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

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Q: 1. Find the natural domain f(x) = 3 √2x+1

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Q: f(x) = 2 - 1x + 1 4 (x - 4)2, x + 16, x ≤ 0 0 <x

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Q: Let f(x) = V9 + x. Find f(3V5) ·f(-3V5)

A: Given: fx=9+x

Q: The revenue function for Sunny Electronics iSun media player was modeled by…

A: The revenue model is given by R(t)=(2000t−100t2)(100−t2) where t = time in months…

Q: : Let f(x)=el-x. Find f'(x).

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Q: Let f(x) = V3x +4.

A: