State where the power series is centered. Σ (-1)"(x – 47)6n (6n)! n = 0

Q: Answer the given DE below: x (dy/dx) +y=y^2

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Q: Evaluate the limit. If dne, explain. (2cos(4x² + 7) + [6x² + 4] lim X→+∞ 4x2 + 7

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Q: If the solution to fe sec (ex**)dx is equal to k tan(e**) + C, find the exact value of k 1. 2e 2e (0...

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Q: In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try...

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Q: 8lnk k k=3 WI

A: Follow the procedure given below.

Q: dx The integral S ex+1 reduces to f k au, where u = f(x) and for some constant k . Compute f (1).

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Q: Find the indefinite integral. J. x cos 107Tx2 dx

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Q: Solve the initial value problem. d²y = 2 e -X, y(0) = 0, y'(0) = 4 dx

A: ∫ d2ydx2 =∫ 2 e-x dxdydx=2e-x(-1)+Bdydx=-2e-x+B ...(1)

Q: Exercises 1. Verify formula (2) of Section 50. 2. Obtain and verify formula (3) of Section 50. In Ex...

A: We have to find general solution of given differential equation.

Q: The average daily temperature at a tourist lodge is approximately T = 106 - 34 cos[ ( 4π ( t - 50 )...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: y = Cax+) ?x5+3 (3メ+)% (4xx+)

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Q: function f(x) is given.  f(x)=log2 (log5 (x)) a)find the domain of the function f. (enter your ans...

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Q: A plane flying horizontally at an altitude of 2 miles and a speed of 460 mi/h passes directly over a...

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Q: 1 dx cos x 7. . /3 1+sin x 8. cos rsin r dr. 9. cos rsin?r dr. COS

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Q: what is the range of h(x,y)=ln(x+y-5)

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Q: 1. lim G3th)g

A: Evalute limh→0-3+h2-9h

Q: Plot the following functions 1. y = - V2x +1

A: x y=-2x+1 -12 0 0 -1 1 -3 2 -5

Q: Solve the following differential equation (y-4x-1)²dx-dy=0

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Q: IUS IIIteTval of Converger Approximate In(0.5) using the first 5 terms using the expansion.

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Q: Evaluate the integral. 15e cos(2x) dx

A: To evaluate the given integral

Q: 3 1 dx x2

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Q: Q1: Find the slope-intercept forms of the equations of the lines that pass through the point (3, -4)...

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Q: Find the differential equation whose solution is given by: y^2 = 4ax

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Q: x² + y? = r2 O y = - y' = - y

A: topic - differential equation

Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

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Q: if 4x1

A: Given problem:-

Q: Prove that 2"+l > (n + 2) · sin(n) for all positive integers n.

A: We have to prove that, 2n+1>(n+2)·sin(n) for all positive integers n.

Q: dy/dx+3y=2

A: Given query is to find solu of the differential equation.

Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x) 

Q: The sum of the series E-1 1-2n is: A) 1. B) 2. C) : D) 3

A: Here we have to find the sum of series ∑n=1∞121-2n

Q: du Compute f ) CSC X If u = f(x), then dx sin x - cos x %3D B 1 -1

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Q: 5 sin Od0 = -5(cos x – 1). Select one: O True O False

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Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos 4x-...

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Find f (x) so that when u = f(x) the integral J tan(f(x) 1+ In x dx can be rewritten as cot u du. %3...

A: ∫1+ln(x)tan(f(x))dxlet u=f(x)=xln(x)⇒u=xln(x)differentiate on both sidesdu=(1+ln(x))dx

Q: th th 1. The 6 term of an A.P. is -5 and the 10 term is -21. Find (i) the 8th term (ii) the sum of t...

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Q: y =-1 2х

A: Given functiony=12x-1

Q: If the solution to ſe2* sec²(e2*+1)dx is equal to k tan(e2x+1) + C , find the exact value of k... 1 ...

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Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting integra...

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Q: 3. What transformations have taken place, of the parent function, to get to f (x)? Describe in words...

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: Let length of one piece be x, then the length of the other piece will be 48−x.

Q: т?+2m Consider dm. If we let u = m + 1, what will be the resulting integral as a function of u? m+1

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Q: Consider S dx and using u-substitution in rewriting the integrand as a function of u and du. Determi...

A: topic - indefinite integral

Q: solve the equation over the interval [0,2\pi ) ). (5sin(2x) 5cos(2x))^2=25 x=__________

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Q: 2. @-2-6X8-マメーメー3メー6時+2

A: f(x,y) = 2x2-3y-4∂f∂x =ddx(2x2-3y-4)∂f∂x=4x∂2f∂y∂x =ddy(∂f∂x)∂2f∂y∂x =ddy(4x)∂2f∂y∂x =0∂2f∂x2 =ddx(∂...

Q: In a world where people's happiness is the product of the square of the amount of one's food which c...

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Q: Question d²y Find if-x2 + 3y² = 4. dx2 Provide your answer below:

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Q: y" + y " +y' + y = 1

A: A differential equation is said to be linear if no terms in it are formed by multiplication of two t...

Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

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Q: Solve the initial value problem for x as a function of t.. dx (? - 15t + 56). = 1 for (t> 8), x(9) =...

A: Given that      (t2-15t+56)(dx/dt) = 1 for (t>8), x(9)=0 Here we have to find the initial value p...