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Q: f' (x) = 8. ニ |8x-9|

A: Given that: The function is f(x) = ln 8x - 9 .

Q: Calculus Question

A: u=7+x4  .........equation (i)differentiate wrt x on both side dudx=4x3du=4x3dxdu4=x3dx .......equati...

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx...

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we dif...

Q: Solve using solutions to first order differential equation.

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Q: nd the interval of convergence for the given power series. (Use INF for +o and MINF for -00 ). (2k)!...

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Q: Evaluate the integral. 7/3 8 sec 0 tan 0 de T/4

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Q: Passing through (-1, 3) and parallel to the line whose equation is 3x - 2y - 5 = 0.Use the given con...

A: Given:  3x-2y-5=0  

Q: Integrals Evaluate each integral.

A: The given integral is .∫coth2xcsch2xdx.

Q: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−254

A: Focus of the parabola is -394, -4 and directrix is x=-254. Now, Focus=-394, -4⇒h+p, k=-394, -4⇒h+p=-...

Q: Find the derivative of the function. r (x) = 3x 20.6 8. -8 - 6. 6x1.6 2]

A: The derivative of a polynomial function with degree n:

Q: Rationalize the numerator : (√x + √y) / (x2 - y2)

A: The given expression is x+yx2-y2

Q: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15 an...

A: Given: f(x)=x+1 at a=15

Q: Solve the differential equation given the condition P(1)=5   dP/dt = 5(sqrt(Pt))

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Q: Consider the power series Find the center and radius of convergence R. Center a = Radius R = What is...

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Q: Consider the first order partial differential equation x*uz – Uy = e³". (a) Find the general solutio...

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Q: I need help with this ones

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Q: I need help with 20

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Q: #13 The radius of a sphecical blloon is increasing at the cate of 3inches per second, How fast is it...

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Q: Find the area of the surface generated by revolving the curve y = 2√x, 1≤x≤2, about the x-axis.

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Q: Solve the system using Cramer's Rule. 4x 5y = - 14 3x - y = 1

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Q: Write ∫ tan5 x dx in terms of ∫ tan3 x dx.

A: Write ∫ tan5 x dx in terms of ∫ tan3 x dx.    

Q: Find the infinite sum, if it exists for this series: −2+(0.8)+(−0.32)+⋯-2+(0.8)+(-0.32)+⋯

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Q: Evaluate the integral. 3 + 7 cos? 0 de cos? 0 /4

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Q: A constant force F=9i−1j+8k moves an object along a straight line from point (7, 10, 10) to point (-...

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Q: Evaluate the integral.

A: The given integral is ∫1+ex2exdx.

Q: Find the time required for an investment of 5000 dollars to grow to 8100 dollars at an interest rate...

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Q: A Ferris wheel has a radius of 26 feet and travels 7 feet every second. At what constant angular spe...

A: b. Radius of the wheel is 26 feet. Circumference of the wheel is C=2πr=2π×26=52π ft 7 feet is travel...

Q: If f(x)f(x) is a linear function, f(−4)=−4, and f(2)=4, find an equation for f(x)f(x) =

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Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced t...

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Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller ...

A: The amount of fencing required would be equal to the sum of length of all the sides including the pa...

Q: Differentiate (1 + x2) arctan x-x.

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain afte...

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an answ...

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Q: Find all values of the variable a for which the rational expression is undefined. 4x + 19 T2 + 13x +...

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Q: Calculate the following integral

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Q: Find the x-coordinates of all points of inflection, and find the open intervals where the function i...

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Q: log7(3x)=2

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Q: et f : R → R such that f(x) = 6x° + 5x* + 2(x log x)² + 7. Determine if f(x) is O(x°) and prove your...

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Q: Find an equation for a circle with center (-9,2), tangent (touching at one point) to the y-axis. Ay ...

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Q: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.  

Q: For her exercise today, Lashonda plans to both run and swim. Let r be the number of laps she runs an...

A: Here we want to find the inequality representing the given situation.

Q: Eactor completely - 1/4 (x+2), ー14 x 114 -114 (x+2) +x

A: Given,          x-14x+214+x-14x+2-14

Q: Find the interval of convergence for the given power series. (Use INF for +o and MINF for -∞

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Q: A tree grows at an angle of 5° from the vertical due to prevailing winds. At a point d = 41 meters f...

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Q: Suppose g is a function which has continuous derivatives, and that g(7)=3, g′(7)=1, g′′(7)=5, g′′′(7...

A: Taylor series of any function with center x=a is  f(x)=f(a)+f'(a)(x-a)+f''(a)2!(x-a)2+f'''(a)3!(x-a)...

Q: Question a and b

A: Given function y - y = x+1+x24Differentiating with respect to x to find dydx,dydx = ddxx+1+x24dydx =...