How is the series 2 + 6 + 10 + ... + 86 represented in summation notation? 21 Σ(4k + 2) k=0 21 Σ(4k + 2) k=1 28 k=1 (3k + 2) 28 Σ(3k + 2) k=0

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: To find the inverse Laplace transform.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = et cosh t L{f(t)}:…

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Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: f a function is increasing, then will using left or right endpoints overestimate the area under the…

A: Let's solve.

Q: 1. Write a list of angle degree measurements between 0° and 180° whose sin value can most easily be…

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Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: 2. (a) If z = 1+ 3i and v = −2 − i then 1 A. + 2 B. Tin Tin + C. A. 2√6 e-in/6 B. 2√3 e-in/3 D. 2 10…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given, L-12s-1s32

Q: Use the Laplace transform to solve the given initial-value problem. y" + 5y' + 4y = 0, y(0) = 1,…

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Q: A parabola can be drawn given a focus of (-4,-10) and a directrix of y = -2. Write the equation of…

A: I am attaching image so that you understand each and every step.

Q: For u(x, t) = f (x + ct) + g (x – ct), where c is a constant, find ux, ut, uxt . Show your work…

A: Given, u(x, t) = f (x + ct) + g (x – ct)

Q: TT secx dx cot 3x

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Q: If s(t) = 3t2 – 2t – 1, then s(-1) =

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Q: Use the Root Test to determine if the given series converges absolutely or diverges. ∞ Σα 1 ( 9) n…

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: 2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

Q: Let k>0 be a positive constant. Find where Cis the arc of the parabola is a constant, from the point…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Given, f(t)=t2e-4t

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 2n +4n in (2n) X

A: Follow the procedure given below.

Q: 9) Write an algebraic expression for the following cos(arctan 2x)

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Q: Explain why a circle of radius 4 cm and a circle of radius 13 m have the same number of radians?

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Q: A population of 480 bacteria is introduced into a culture and grows in number according to the…

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Q: Find the product of (8 + 6i) and its conjugate. product =

A: solution:-the complex number is 8+6i the complex conjugate of 8+6i is 8-6i

Q: Evaluate the following integral or show that it is divergent. 0 -√x VX dx

A: Explanation of the answer is as follows

Q: 1. (a) First find the following indefinite integral A. e666 B. 2e667 (e - 1) e√x+666 [= √x dx = (b)…

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Q: tan(x) 5. Compute the limit for lim x-0 sin(x) , and show by hand how MAPLE obtain the results.

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.)…

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Q: S A. sinxcosxdx √esc²x-1 2 B. 7 COS X 7 5 COS X 5 5 cos³x x + C X 5 7 COS X 7 +C C. D. sin7 x 7 5…

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Q: Write the equation of the line shown. Be sure to use the correct variable. Equation:

A: NOTE: Refresh your page if you can't see any equations. . the given graph is as we can see the given…

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 20-x²;…

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Q: 3. A wheel has a diameter of 70 cm and completes a revolution in 0.25 seconds at top speed. a.…

A: Angular velocity= θ/t , θ= 2π×number of revolution per unit time  Linear velocity= radius× angular…

Q: 2 3. Prove: sinx + sinxcot x = cscx.

A: I have stated the used formulas in the solution

Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = e-t cosh(t)

A: NOTE: Refresh your page if you can't see any equations. . take Laplace use the Laplace rule

Q: Find the derivative of the function. y = 2x² +3 x² +1 X y' =

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Q: Can you please specfically tell me what the two intercepts are.

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Q: a. given the functions f(x)=cosx and g(x)=sqrt 10+x determine the value of g(f(pi)) options : sqrt…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 56. Solve the integral of (x + 2y)dxdy with respect to x from x=y and x = y^2 and with respect to y…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = e* sinh t L{f(t)}…

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Q: J 2 (x+2) dx (x-1)3

A: Given :∫23x+2x-13dx

Q: 8. Prove: 2 1-tan x 1+tan²x cox2x.

A: (1-tan2x )/(1 +tan2x ) = cos2x here we have to compare the left hand side and right hand side apply…

Q: Evaluate the indefinite integral: S √4x + 9 dx

A: Given.

Q: 6) Find the domain of the given functions (use interval notation) and the find f(g(x)) f(x) =…

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Q: Consider the following. f(x) = tan(x), (-1) (a) Find an equation of the tangent line to the graph of…

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Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: ft=t,0≤t<70,t≥7

Q: Determine the interval of convergence of the given power series. n xn Σn=0 9nen Provide your answer,…

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Q: 5 1 So (125 + 25x + 6) dx 6o S X (1 + x²)3 dx / 1 + x² dx 1

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Q: 8) Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: what

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: To find an equation for the function f that has the given derivative and whose graph passes through…