Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what is f(5)?

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A: differential equation

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Q: 8. . cos?rsin®x dx. COS 프2

A: Product Rule of integration : ∫u.v dx = u∫vdx -∫(dudx∫v.dx)dx dsin(x)dx=cos(x)  and dcos(x)dx=-sin(x...

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Q: Find the indefinite integral. sin 78 V COS 76 de

A: Given: I=∫sin37θcos7θdθ  ....(1)   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1

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Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

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

A: By using the definition of Taylor series to find the Taylor series centered at c for the given funct...

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Q: Using integration by parts and taking a > 0, the integral S x In(ax)dx is equal to:

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Q: Question

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Q: Given f''(x)=7x+6 and f'(−1)=−1 and f(−1)=1.   Find f'(x)=    and find f(3)=

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Q: C. Determine the value of a and b that make the given function continuous. (Choose one) ax + b x1 ах...

A: Topic:-  limits and continuity

Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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Q: Integrate S (a?- ) dv ; where " a" is constant O = - + C 3 =-{ (a? – v²)* + (a? – v²)* + C O = (2? –...

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A: ln(a/b) = lna - lnb

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Q: 1. Which of the following argument is an example of deductive reasoning? *   a. John got a perfect s...

A: As per bartleby guidelines we only give first three question answers. 

Q: 12. Simplify the following rational expression for the function f (x) = 5x2 f(x + h) – f(x) h

A: Given f(x)= 5x² So, f(x+h)= 5(x+h)²=5x²+10xh+5h²  

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Q: In a certain electronic factory, the ratio of the number of male to female worker is 2:3. If one hun...

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Q: You are given the graph of a function f defined on the indicated Interval. Find the coordinates of t...

A: Absolute Maximum of a Graph: The absolute maximum of a given graph is the point on the entire graph ...

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Q: The function f(x,y) = 2x + 2y has an absolute maximum value and absolute minimum value subject to th...

A: The given function is; f(x,y)=2x+2y and the given constraint is ; 9x2-9xy+9x2=16.

Q: What are the removable singularities of the functions ?

A: Topic:- function

Q: 7. 4. A firm's marginal cost and revenue functions are given by MC- 12e + 16a + 20 MR = 100 -29 a. R...

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Q: 3.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it....

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Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: 4) Find the interval of convergence for the power series Σ (-1)"-1п 2n n=1

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Q: Question The derivative of the function tan(In(vx² – 6x +1)) is: -

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Q: Find the in tervals on which f are: (il In creassing and decreasing Con cave uP and con cave down an...

A: Here, the given function is: y=sin22x, [0,π]

Q: 4.(Straightforward) Make the differential equation below exact by find- ing an integrating factor u....

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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: (3+2 v5)(6 - 2 V5) (4 – V5) (a) Simplify giving your answer in the form a+bV5, where d integers.

A: In this question we have to solve the following question.

Q: y y 12 12 10 8 6 4 2 21 X 2 4. 8 10 12 4 (d) Show that the slopes of the graphs of f and f are recip...

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Q: ontinuous Limit   f(y) =  20y + 13, if  y ≤ 4            (y + k)² + t, if y > 4 k & t is constant...

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Q: Order the functions from slowest growing to fastest growing as x -o: 4x², (In x)³, 10*, and e2x

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Q: Find the radius of convergence and the interval of convergence. k(k + 10) k=1 Radius of convergence:...

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Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

Q: III. Answer the following questions. 1. A window in the shape of a rectangle surmounted by a right t...

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Q: Solve the given initial-value problem. dy + y = In(x), y(1) = 20 dx (x + 2) y(x) = Give the largest ...

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Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6