If ſ²₁ f (x) dx = 3 and ²₁ g(x)dx = 8, find §²₁₂[4ƒ(x) — 2g(x)]dx -1 -1

Q: 3+x 4. (a) Find a power series representation for the function f(x) = is the radius of convergence?…

A: The given function is

Q: If f(x)=sinx+ 2 cosx-x, find / (1)

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Q: A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 2 m³/min (see…

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Q: We have found the following Maclaurin series. x4n 142n (2n)! Now we can use this to find the…

A: The given function .The aim is to find the Maclaurin series of the given function.

Q: elow, we see a region bounded by two curves. (graph not necessarily to scale)

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Q: What is the Rank of the following matrix? 325 65 13 30-1 OA.O OB. 1 OC.2 OD.3 QUESTION 2 Fill in the…

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Q: 2. Consider the following three points (a) (b) ( (c) P= (1, -3,1), Q = (2, 1,0), R= (1,0,1) Find the…

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Q: A sports watch has a price-demand equation given by p = D(x) = 50.2-0.0567142x dollars, which gives…

A: I have appended the formula used in solution procedures

Q: Find the exact slope of the tangent line to the parametric curve x= 4 cos(t) y = 8 sin(t) at the…

A: {x=4cos⁡(t)y=8sin⁡(t) at the point where t=π6

Q: 4. The financial department of a hospital arrived at the cost function: C(x)=20x³-360x² +2300x-1000,…

A: Given cost function is

Q: Suppose an> 0 for n≥1 and lim wan = 1 n-x What can you conclude regarding Σα1 an? n=1 The series…

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Q: Evaluate the indefinite integral as an infinite series. | arctan(x3) dx ]) + c C ( n = 0

A: The given integral .The aim is to solve the indefinite integral as an infinite series.

Q: Find the general Solution For D-E (xy-4/nx+x² sin x²) dx + x² dy =o

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Q: 9. The radius of a large balloon is increasing at a rate of 2 inches per second. How fast, in cubic…

A: Let r be the radius of the balloon and V be the volume of the balloon That is we are to find the…

Q: ne whether n=1 1 is n(ln(n) + 1)²

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Q: In the following exercise, given that 1 1-x = ∞ Σa x" for x < 1, n=0 use term-by-term…

A: Power series.

Q: Use power series operations to find the Taylor series at x = 0 for the following function. cos²x…

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Q: Use the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms.…

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Q: 1 x + 1 rectangles and right endpoints as sample points. Rn 0.6345 Estimate the area under the graph…

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Q: Calculus 1

A: z=2x2+xyx=cost, y=2sint

Q: Given that f(x)=4x-16 where f(x)=y define a function rule for f^-1. which of the following are…

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Q: Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded…

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Q: olve the following integration:- 2 x² + 3 x(x-2)(x-6) ² dx

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Q: A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min ​(see…

A: The hemispherical tank of radius

Q: tan x dx

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Q: Find the two solutions of the given equation z² + 6z+ 10 = 0. / in your answers should be positive Z…

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Q: dx Assume that x = x(t) and y = y(t). Let y = x + 2 and dt dy Find when x = 3. dt dy dt (Simplify…

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Q: Find the flux of the vector field F = out of the closed surface S bounded by z = 5-√√x² + y² and z =…

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Q: Let P(t) represent the number of grizzly bears in a population at time t years, when t ≥ 0. The…

A: P(t) is increasing at a rate directly proportional to 600-P(t)P(0)=400

Q: A) lim x²-x+1 5/3 x+2 3

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Express the limit as a definite integral on the given interval. 72 Part 1 of 2 lim Σviln(2 + x) Δ.,…

A: The definite integral  can be written in a limited form on the interval [a,b] as

Q: Find the general Solution For D. E x² dy + x(x+2) Y = ex dx

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Q: pлd¹ The rate of flow, Q of a fluid through a pipe of diameter, d and a length, L'is given by Q…

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Q: Find the general Solution of: dy dx XsinX

A: The differential equation given is

Q: Find the area of the region bounded by the graphs of y=e4, y =e-¹ª, x = -5, and x = 2 using…

A: We have to find the area bounded by curves

Q: Find the points on the curve x = t² - 16t – 5, y = t² + 14t + 7 that have: A. a horizontal tangent…

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Q: Find the radius of convergence, R, of the series. √n R = 00 I = n = 1 6″ _(x + 4)" Find the…

A: The given series is sqrt(n)(x+4)n

Q: Use synthetic division to divide. Express your answer in the appropriate form. (2x²-x² +6x+9) +(x+1)…

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Q: The population of a country in 2010 was approximately 32 million with an annual growth rate of…

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Q: Problem 2: Given the function below, please find the maxima, minima, and the intervals where the…

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Q: ["h h(x) dx such that A expresses the area of the region between the functions y = el.5, y =e-1 and…

A: To write an integral in the form  such that A expresses the area of the region between the functions…

Q: Find the distance d between the complex number - 2 + 4i and 0. d =

A: To find the distance  between the complex number .

Q: 10) tan x = 3.7 A) 1.31, 4.45 1.31, B) 1.31, 2.88 C) 1.31, 4.97 D) 1

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Q: PLEASE PLEASE HELP ME WITH THIS QUESTION, The x y-coordinate plane is given. The curve starts at the…

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Q: he approximation ex = 1+x+ - is used when x is small. Use the Remainder Estimation Theorem to…

A: Given approximation ex =1+x+(x2/2).We have to find error in this approximation by using remainder…

Q: Find the general Solution For D- E dy dx ty cotx= 5 cosx

A: Given to solve DE +ycotx=5e^cosx

Q: Can you please answer question e and g?

A: e) From the graph it is clear that:LHL = Left hand limit at x=3: limx→3− f(x) = -4RHL= Right hand…

Q: Given that /1 3 - 3م = ex dx + (ی - آe)3 - e, use this result to evaluate 3 3ex + 4 dx.

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Q: Determine the slope of the tangent line, then find the equation of the tangent line at t = 36. x =…

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Q: Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = m/2. Use four approximating…

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