f(x) = cos² (3x + 1) − sin² (3x +1) f(x) = ln 1-sin 2.7

Q: x^2) on [0, 1]. A) Find k such that f(x) is a probability density function. B) Find the expected…

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Q: 3. Use the definition of Taylor series to find the Taylor series centered at a = 1 for f(x) = ln x

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Q: Suppose that we're making and selling some widget and the revenue (in dollars) when making a widgets…

A: The objective of this question is to find the average revenue, marginal average revenue functions,…

Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: Find the limit of the sequence an = (cos.n) 5"

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Q: Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and…

A: We have to determine the intervals at which the function  is increasing or decreasing.

Q: Evaluate the integral: 0 x = (A) Which trig substitution is correct for this integral? Ox= 16 sin(0)…

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Q: Write in terms of sine and cosine and simplify the expression. cos A - 2 sin A cos A cos² Asin² A +…

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Q: Use the information given below to find sin(a-B). tan a = with a in quadrant 1 12 5' sinB =15, with…

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Q: Find the equation of the tangent to the curve cos²x - sin²x y = at the point where x = I |4

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Q: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

A: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

Q: S(3x+1) (3x²+2x+1)³dx

A: I=∫(3x+1)(3x2+2x+1)3dxSubstitute 3x2+2x+1=u

Q: Write (but do not calculate) the integral that gives the volume of the solid bounded above by the…

A: We need to find out the integral that gives volume of the solid bounded above by the surface and…

Q: What substitution(s) would make the following integral simpler? I.e., simple enough to integrate by…

A: As per the Bartleby guidelines, answering only first question.

Q: Find the exact length of the curve described by the parametric equations. x = 8 + 3t², y = 7+2t³,…

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Q: 2. Show that the series converges by the Alternating Series Test (two conditions). Then find how…

A: The given series is

Q: An angler hooks a trout and reels in his line at 5 in./s. Assume the tip of the fishing rod is 11 ft…

A: We are to find the change in horizontal distance of the fish from the angler. When it is 17 ft away…

Q: * Fmd the general solution of :- dy dx = (x²+ 3) + x² 3 2

A: To find the general solution of the following differential equation.

Q: 3. Which of the following statements about the function y = f(x) graphed here are true, and which…

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Q: Find the areas of the shaded regions in

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Q: Find the area bounded by -π y = 2 sin x, y = tan x from ≤ x ≤ 37. 3 Round your answer to the…

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Q: Evaluate the integral: 16 √ 2² √² + 64 0x = (A) Which trig substitution is correct for this…

A: We have to evaluate the integral using trigonometric substitution.

Q: A cone is designed to have a radius of 6 cm and a height of 9 cm, but the radius and height are off…

A: Radius= 6 cmHeight= 9 cmChange in radius is 0.03Change in height is -0.06

Q: Combine the integrals L 19 if (6² 1 (3x3-4x²+6x-2) dx + 7 1 into one integral 2 (6x4–3x³ + 10x²+ 8x…

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Q: Compute the electric charge on the surface which is the portion of the cone z = √√3x² + 3y2 in the…

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Q: We are interested in the first few Taylor Polynomials for the function f(x) = 7e² +6e¹ centered at a…

A: We need to find tylor polynomial.

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: The polynomial p(x) = 8x³ - 18x² + 7x +3 has exactly 3 zeros. If p(1)= = 0, use synthetic division…

A: Given that the polynomial

Q: 2. Σ. 1 (-5) 2n n2gn

A: The given series is The Root test If L<1 then series is absolutely convergent If L>1 then…

Q: Let f(x) = f sin t² dt. Find f'(x) x² 2x 2x sin(x4) - 2 sin(4x²) sin(x4) — sin(4x²) 2x cos(x) - 2…

A: Let .To find .

Q: 7. Linear Algebra - Linear Equations 2 Which of the following statements is true about the solution…

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Q: 5. Calculate the following limits: x-5 a. lim x-5x2–25 b. c. d. lim x--5 x²+3x-10 x+5 t² +t-2 lim…

A: 5)a) limx-5 (x-5)/(x2 -25)b) limx-(-5) (x2 +3x-10)/(x+5)c) limt-1 (t2 +t-2)/(t2 -1)d) limx-(-2)

Q: √(x ³ ex² + 4x + ex¹ +4x) dx.

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: Find the Maclaurin series of the function f(x) = (4x²)e-³x ∞ (f(x) = Σ cnan) n=0 C1 C3 C4 C5

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Q: Consider the function defined by f(x) = sin(sqrt(|x|)).  A) What is the domain of this function?…

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Q: Take the logarithm of both sides of the equation and expand it using the product rule of logarithms…

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Q: e Six dx xX (1+lux)

A: We use the method of substitution to evaluate the given integral

Q: 12x 8 °-x X ³/₂ dx 3

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Q: Find the slope of the tangent to f(x) = e" + 1 at the point (0,0).

A: Given that the function we have to find the tangent line at the point (0,0)

Q: We turn now to the problem of finding area under a curve. Suppose we want to find the area between…

A: As per guidelines we can solve only 3 subparts if multiple subparts are posted. So I am solving…

Q: 1 7. Ση=0 (2n+1)!

A: The given series is

Q: 17. Suppose you want to fence three sides of rectangular region where one side is bordered by a…

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Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The graph of the function g(x) is shown as,Since parts a to c are already solved in original…

Q: Below is the graphs of fox & gcx), & their tangent lines at x=2. fy=1.8(x-2) 9 9= ²/3 (x-2) a) lim…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: 2. Find the domain and range for these functions: -2-1 y=fle

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Q: The function f(x) = x 4 has a Taylor series at a = 1. Find the first 4 nonzero terms in the series,…

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Q: Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)…

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Q: Find a simplified series representation of x²e4 answer = n

A: The given function is x2e4x.

Q: (a) Evaluate the integral: S = 16 x² + 4 dx Your answer should be in the form k, where k is an…

A: Since you have posted multiple questions we will provide the solution only to the first question as…