Find the derivative of 27e-5t. O-135e5t O 5e-3/5t O 15e-5t O-5e-5/3t e-5/3t

Q: 1 Let f(x)=x²e² the value of — lim [ƒ(x)]¹/* i is: a) b) 1 d) 1 e c) 0 1 -19 4e

A: Given that a function f(x) and we find the value of limit.

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A: We have to evaluate the integral.

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A: The position function is The slope of secant line passing through points

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A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Simplify (3 — 5x)4(x²y4)³z6 2–³ (27x6)¹/³ (3 — 5x)−³y4z−²

A: Given Expression

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Q: Use the method of integrating factor to solve the following differential equation: y'+y=e-x

A: Thw given differential equation is

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A: The given integral is

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Q: 8.) Evaluate the following limits, justifying your answers. √x-2 X-4x²-16 a.) lim

A: L=limx→4x−2x2−16

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Q: 14.) Find the explicit solution to the differential equation = 4x³y² that satisfies the initial…

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Q: (n75)”. What is the limit of $₁,? (C) e (D) 0 Let (sn) where sn = (A) The limit does not exist (B)…

A: given that

Q: Sorry, I forgot to specify. Can it please be solved algebraicly. I do not want the derivative.

A: The given limit is .The aim is to calculate the limit algebraically.

Q: 1₁ 4 tan x sec x dx I

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A: we have given a function

Q: 3) Using the Fundamental Theorem of Calculus (FTC), find the exact values of the following definite…

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Q: Compute the indefinite integral S dx 8x4 Remember that you must wrap any functions such as sin (x)…

A: The given integral is .The aim is to solve this integral.

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Q: A tank initially contains 60 to the tank at 1 gal/min, ar quantity (g) of salt at time

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Q: Find the integral. 9e 0.2x dx. O 45e0.2x + C O 9e0.2x + C O 9e0.2x + 1 0.2x + 1 + C O 18e0.2x + C

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Q: Consider the initial value problem y" + 25y = 2 cos(5t), y(0) = 0, y (0) = 0. a. Take the Laplace…

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Q: Find the area bounded by x=0, y=x, x=1 and y=x² by using double integration method

A: We need to find the area bounded by the curves given by :

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Q: 9. x+5 5x X-5 x+-

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Q: B: Find General Solutions for the following Differential Equations (Use Differential Operators) (D²…

A: we have given differential equation

Q: 10. Find the radius and the interval of convergence for the following power series. (x - 3)" n² n=1

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Q: S 9 x²+25 -dx

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Q: ро b) Point P (3, 7) is in coordinate. Express this point in cartésion coordinate

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Q: Question 1.1 Determine the laplace transform for the following function: f(t) = 9t²-7t+1 that is…

A: Consider the given function  We will use the formula

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Q: Consider the initial value problem y" + 4y = 8t, y(0) = 4, y (0) = 8. a. Take the Laplace transform…

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Q: Use the guidelines in this section to choose u that should be used in integration by parts for the…

A: Given Formula :Now we have to evaluate by using this given formula.For this purpose we choose

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