Find the derivative of the function. f(x) = 6(x³ + x)³

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Q: QUESTION A3 Calculate the test statistic, Z for the population mean.

A: The test statistic is a z-score (z) defined by the following equation. z=(p−P)σ  ,  where P is the…

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A: We have to find out

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Q: Which of the following is the derivative of f(x) Select one alternative: ○ f'(0) 1 h→0 1-h ○ f'(0) =…

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Q: Differentiate f(x) = 5(6x8-8x6) ¹0. You do not need to expand your answer. f'(x) = Factor out the…

A: ddxxn=nxn-1

Q: Σ(1) A k! μέρος

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Q: x²-x-6 x² + 4x+4 x +5 +6 + 6-2x a) Factor and determine the non-permissible values of x. 2. Consider…

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Q: Solve for the general solution: -4 Oy=a³e + co Oy=x³e +cª Oye +³ e* + c³ Oy=x³ee² + c xý – 4y = co e

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Q: 10. Find the Taylor polynomial P4 for f(x) = In x at xo = 1. (a)_1+ ²(x-1)=(x-1)² + ²/(x-1) - 1 4 5…

A: Given f(x)=ln x    x0= 1we want to find taylor polynomial P4(x)

Q: Use the graph at right for questions 4 and 5. It consists of a semicircle and two line segments. 4.…

A: Graph of derivative function f'(x) for a function f(x) does not exist at x=c iff f(x) is not…

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Q: Given the function f(x) = x³ + 3x². 9x+5 over the interval −7 ≤ x ≤ 2, answer the following…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 3-2.…

A: We need to find width and height.

Q: 55-58 Find equations of the tangent line and normal line to the curve at the given point. √√x x + 1'…

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Q: Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x) = −2x(2x² +…

A: Given; We know that the y-intercept is an (x,y) point with x=0. So, we get that f(0) = 0.

Q: The line that is normal to the curve x² + 4xy-5y2 = 0 at (4,4) intersects the curve at what other…

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Q: Consider the function f(x) = 2 - 6x on the interval [-5, 5]. Find the average or mean slope of the…

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Q: find the second derivative of the function

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Q: [2√T S Suppose you use the substitution u = 1+ 3x³ to evaluate the definite integral of the…

A: The given definite integral, ∫01x21+3x3dx We have to find the equivalent expression using…

Q: Which of the following functions is not differentiable on all of its domain? Select one…

A: Let fx=x2-1

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Q: Find the indefinite integral. (Use C for the constant of integration.) Sinces In(e8x - 5) dx

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A: Here we have to find the polynomial.

Q: The form of the partial fraction decomposition of a rational function is given below. A B = Now…

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Q: B E A B Q: ABCD is quadrilateral Shape whose diameters. intersect at E, Sinc AB / CD // EF, and F in…

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Q: Question 15 Find constants 4 and 8 such that the function y Asinx + Bcost satisfies the differential…

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Q: Given the function f(x) = x³ + 3x² − 45x + 8 over the interval -10 ≤ x ≤ 5, answer the following…

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Q: A roast turkey is taken from an oven when its temperature has reached 175 Fahrenheit and is placed…

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Q: If x < 1 (x2 + 1 x - 22 if x 2 1 (a) Find the following limits. (If an answer does not exist, enter…

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Q: Find the area of the region, pictured below, bounded by the curves f(x) = x³ + 2x²-x-3 and g(x) = x²…

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 6 Σ1 4 + 1…

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Q: #37) (modified) Find the equation if the tangent line at the point x=1: y = x4 + 1/x - 3ex

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Q: Recall that the logistic model can be written in the form a) Give the formulas for finding the…

A: We have to find carrying capacity and growth rate, by comparing the logistics model formula to the…

Q: Calculate the sum of the series S n = 2 - 8(0.9)" Σ an n = 1 whose partial sums are given.

A: We want to calculate the sum of the given series whose partial sums are given.

Q: Find a function that satisfies the given conditions and sketch its graph. lim f(x)=2, lim f(x) = ∞o,…

A: The function is not defined when x approaches 5 from left or right. So it must be an asymptote and…

Q: What is the maximum vertical distance between the line y = x + 20 and the parabola y = x² over the…

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Q: ect one anter 110 O √6 36 O√14

A: Topic:- geometry and area

Q: 4. Martin's family drives 300 km from their home to a family reunion. His cousin Sherry and her…

A: Since both reach the party at the same time so both take same amo

Q: 31. At the beginning of a study, a certain culture of bacteria has a population of 80. The…

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Q: The function f(x) = 3 - 2x is defined for the given domain -2 ≤ x ≤ 2. What is the range? (A)7 ≤…

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Q: Problem 4. number, using the following steps. In(x) xxx0.01 (a) Compute lim (b) Compute lim In(x)…

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Q: 5. f'(x) does not exist for x = A. 1 only B. 1 and 2 C. 2 and 6 D. 0, 1, 2, and 6

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Q: Find dy by implicit differentiation. dx dx 11 xey = x - y

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Q: Indicate all critical points on the graph of f in the figure below and determine which correspond to…

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Q: Given the function f(x)=5x^4+75x^3+315x^2+405x, and one of its factors is (x+9), write f(x) as a…

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: Integration

Q: Consider the function f(x)=2x^3+12x^2−30x+7, −5≤x≤2 Find the absolute minimum value of this…

A: Given function f(x)=2x3+12x2−30x+7,We know that, at  critical point x=a ,If f 'x&gt;0 to the left of…

Q: Suppose that the derivatives f'(z) and g'(z) exist. Show: f(z)g(z)-g' (z)f(z) g²(z) b) [f(g(z))] =…

A: Let f(z) be a differentiable function. Then the derivative of a function is defined as…