Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

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Q: af af Find and for the following function. Əx ду f(x,y) = x² - 2xy +9y² af ?x II

A: This question is related to partial differentiation, We will solve it using given information.

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Q: Exercise 195 Further problems on Leibniz's theorem 8. If y = (x³ + 2x²)e2* determine an expansion…

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Q: 1) Solve the initial value problem. Show All Your Work. dy 2x+ sec? У(0) %3 — 5. | dx 2y

A: Let's solve diffrential equation.

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Q: Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to…

A: To find the horizontal and vertical tangents to the given curve.

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A: partial derivative

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A: Given, f(x)=3x+1 To be found : f"'(3)

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Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

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Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: Q1: Find the Laplace of the following Periodic functions: 1. f(t) = t 0 <t< 2 2. f(t) = ksin(wt) 0…

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Q: 8. If y = (x* +2x²)e2* determine an expansion for y(5). %3D [y(5) = e2x24(2x³ + 19x² + 50x + 35)]

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Q: e* (1-e*) (1+х) [Iin(1-х)] 12. lim,»0

A: LetL=limx→ 0ex1-ex1+xln1-xplug x=0L=e01-e01+0ln1-0L=11-11ln1L=1.01.0L=00Which is undetrminat…

Q: For the function f(x.y.z) = 1+ xy° - 4z*, find f f, and f.

A: We can find the partial derivative in the following steps.

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A: In order to get g(t) integration need to be done.

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A: See this solution in below

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A: Integration need to be done after proper simplification of the term.

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Q: the answer is incorrect is not 64pi

A: see below the answer

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Q: Q3: Find f(t) ( Inverse Laplace Transform )of the following functions s+1 2.F(s) = s4+s2

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A: In order to find the first five terms, we need to apply the formula of Tailor's series entered at 2.

Q: 5s F(s) %3D (s + 7) (s? + 4) 35 35 10 -7t Answer: f(t) G, cos2t + sin2t) 53 %3D 53 33

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: 1. Find for each of the following: dx d) y = e +x* +e° g) y =x2r-5 h) y = log3

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