Use the Laplace transform to solve the initial value problem below: b) y" + 3y' + 2 y = f (t) Where (1, osi< 10 S(1) = 10, ; y(0) = 0, y'(0) = 0. 12 10

Q: Use the formula for the binomial series: (1 + x)" = т(т-1) 2 2! m(m–1).-(m-k+I),k + + 1+ mx + %3D .....

A: The maclaurin series for 1+x7

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 00 5+ 2"...

A:

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increas...

A: Given :Radius of thr ripple increasing by 2 feet per secondCircumference = 2πr

Q: create a graph with labels of a function that have one point where f(x)=-3, at least one local minim...

A:

Q: Find the derivative of the following function using the limit definition f(z) = 2z4 − 4z2 . Find ...

A: f''(z) derivative of the function  f(z) = 2z4 − 4z2  using the limit definition

Q: Power Rule Give 3 examples with solution and final answer. Make sure it is unique and not advanced.

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Q: 18. Use logarithmic differentiation to find the derivative of y with respect to the given independen...

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Q: Assume y(x) eaa cosBx is one of the solutions of the DE y(3) – 3y" + 7y' – 5y = 0. - Then α β (A) 3 ...

A: The given question can be solved as shown in step2.

Q: Evaluate the following integrals with solution

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Q: Solve the triangle for which ZA = 30\degree, ZB = 45\degree, and a = 20. Round to the nearest whole ...

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Q: Find the derivative of the function. S(2) = VE - 8E f (x) =

A: topic - derivative of a function

Q: f(x) Find g'(3) given that f(3) = -6, f'(3) = –4 , and g(x) = %3D %3D 8 Answer:

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Q: Solve the triangle for which ZA = 30\degree, ZB = number. Do not use a decimal point or spaces in yo...

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Q: Verify that the indicated function y = Q(x) is an explicit solution of the given first-order differe...

A: Solution : when y=125-x2y'=-125-x22×-2xy'=2x25-x22y'=2xy2thus in terms of x,2xy2=dydx

Q: A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the s...

A:

Q: Compute T (æ) at a = 0.9 for y = e" and use a calculator to compute the error le – T2(x)| at a = 0.5...

A: Find your answer below 

Q: A lighthouse rotates its light in a circular motion with a constant speed. If the beacon of light co...

A: Given ,  A lighthouse rotates its light in a circular motion with a constant speed If the beacon of ...

Q: 6. State the quadrant bearing and true bearing of the vector shown: Quadrant Bearing 25 W + E True B...

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Q: If Y=tanx prove that %3D2

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Q: 9. Given the vector ū =[-2,3,–4] a) Draw the vector. b) Determine a unit vector collinear with ū. y

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Q: Answer the following questions for the function f(x) = - 8x° - 36x? +240x – 11. ... a. Find formulas...

A: Topic = Derivative

Q: Given f''(x)=−9sin(3x) and f'(0)=4 and f(0)=−1.   Find f(π4)=

A: Topic:- application of integration

Q: What value should be assigned to a to make the function x<3 |(x) = {x²- 1, (x)%3D (2ax, x23 Continue...

A: Given:   Function equation is given

Q: Find the volume under the paraboloid  z = 4x2 + 4y2,  above the xy-plane, and inside the cylinder  ...

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Q: Find the exact value of the expression, if it is defined. (If an answer is undefined, enter UNDEFINE...

A: topic- trigonometric ratios

Q: Y = e-5x x > 0

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Q: Determine whether the series is convegent or divergent. If it is Convergent, find its Sum, 8) nニ2

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Q: 7 sin(t) + tan(t). tan(t)

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Q: JA 1 J 40. f(x) x'+3x + 7

A: Given query is to find the interval where function is increasing and decreasing.

Q: 00 Suppose that anis an infinite series with partial sum SN= 7- 10 16 What are the values of anand a...

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Q: A large hotel chain needs to apportion 35 new surfboards for its visitors to rent among three hotels...

A: Given:    Total number of surfboards = 35   Adam's Method:  Step 1 : Find standard divisor,SD  = to...

Q: Compute the work required to stretch a spring from 7 to 13 cm past equilibrium, assuming that the sp...

A: Given query is to find the the work required.

Q: 1 Σ k=1 27k 2k

A:

Q: (b) Given that = 3 in steps of 0.2, given that y = 4 at r = 2. dy = x+Vy. Use Euler's Modified Metho...

A: Given y'=x+yy(2)=4   , y(3)=?       h=0.2  modiefied euler method is yn+1=yn+hfxn+h2 , yn+h2f(xn ,yn...

Q: rt%3Dr/6 t cos(2t) dt t=D0

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Q: x" – 2x' + x = et x(0) = 1 ; x'(0) = 0

A: solution given below

Q: Minimise x + y - 2xy subject to the constraint y 1: Answer:

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Q: UQuestion 2| Differentiate each of the following functions with respect to x a) y = 3x b) f(x) = +5x...

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Q: Find the Mclaurin series for e^x⁴. What is the radius of convergence?

A: the given expression ex4

Q: Find the centroid of the given region. [Give exact answer in fraction form.] y = 2-x? y =x The centr...

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Q: Write the letter of your answer on the space provided before the number. 1. It is well-defined colle...

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Q: A. Describe the set of inputs, the function rule, and the set of outputs for each function. 1. The a...

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Q: 0 2 46 8 10 12 f(r) = 16 14 13 14 16 20 23

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Q: Obtain the general and particular solution 1. 2ydx = 3xdy, when x= 2, y = 1.

A: The given differential equation,1. 2ydx=3xdy, when x=2, y=1 Note:     Multiple questions are given, ...

Q: The Differentiation to be made must be based on the following topics. - Product Rule Give 3 examples...

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Q: Find of the function given implicitly: 6xy + 7e" = 7e . Evaluate the second derivative at the point ...

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Q: 5. Classify each quantity as a Vector or a Scalar. Circle the correct response: a) a car drives 50 k...

A: Topic = Algebra

Q: Use the root test to determine whether the series converges or diverges. If the test is inconclusive...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 5+ 2" 1....

A: