Given that What is F'(x)? O Questi -S²³² F(x) = 3 In t t² +3 25x5 ln x x5 +3 5x² ln x x5 +3 9x² ln x x6 +3 3x² ln x -dt

Q: Evaluate the limit, limx→∞ 3x² e4x

A: L=limx→∞e4x3x2

Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

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

Q: Given the function f(x)=x-7, find the net signed area between f(x) and the x-axis over the interval…

A: Given that the function y=x-7 we have to find the area of the region [-1,9]

Q: The function s= -1³ 31²-31, 0sts 4, gives the position of a body moving on a coordinate line, with s…

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Q: Solve the following Initial Value Problem. dy dt - y= sec² (t) + 3 sin(t), y() = 1

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Q: The amount, A, of 159 grams of a certain radioactive material remaining after years can be found by…

A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WO FOR BETTER…

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Q: Find the radius of convergence and the interval of convergence of the power series. M8 n=1…

A: Radius of convergence is half the size of interval of convergence.And we use ratio test to find the…

Q: Find the sum of the series: Σ n=1 2 (n + 6)(n + 4)

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Q: 4. 14: I can evaluate a definite integral using geometry or the FTo C. The graph of f is [4, 8] the…

A: graph

Q: 2 2 Find the area of the region between the curves y = 4x² - 4 and y=-3x +3 from x= -1 to x= 1.

A: The required area is the shaded region in the graph

Q: If g(s) = * · 86 0 g'(s) = √5 + x7 dx, compute g'(s).

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Q: 3. (a) (b) YA -2- X 0 g(x) Let f be the function whose graph is given below. X g'(x) 0 2 Complete…

A: As per our guidelines, we can solve first one as your both parts are not small. Please repost the…

Q: Suppose f(1) = 2, ƒ'(1) = 3, ƒ (2) = 1, ƒ'(2) = 4, and g(1) = 3,g'(1) = 5,g(2) = 1,g′(2) = 4. If…

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Q: Given the definitions and g(x) below, find the value of f(g(−3)). of f(x) 2 f(x) = x² + 7x + 13 g(x)…

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Q: Sketch the graph of the piecewise-defined function. Write the domain and range of the function. |x,…

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Q: Find all solutions exactly on the interval [0, 27). If there is more than one answer, enter them as…

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Q: lim n→∞ (1 + 1/2 ) ² = 2n

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Q: 10 -9 -8 -7 -6 -5 -4 10+ H Cu Ha STI -10 1 2 3 4 5 6 yak x Write the standard equation for the…

A: The standard equation of hyperbola with transverse axis parallel to x axis is

Q: Ĵ Refer to the graph shown below to evaluate -2 fit) f(t)dt.

A: A graph of the function  is given.The aim is to find the value of .The integral formula  is used in…

Q: Let y = f(x). Begin by finding the derivative of f(x) = -x³ + 6x² - 3. 3 F'(x) = (x³ + 6x² − 3) d dx…

A: The objective of the question is to find the second derivative of the function f(x) = -x^3 + 6x^2 -…

Q: Using the function f(x)=cos(x), on the interval: 0 (less than or equal to) x (less than or equal to)…

A: The objective of this question is to calculate the Riemann sum of the function f(x) = cos(x) over…

Q: 6. Let So f(x) dx = 12, 5 Calculate the following integrals. (a) [°*3f(x)dx = (b) *2f(x) – g(x)dx =…

A: Let To calculate the following: (c) If  is an odd  function, then to find .Note:  Since, the student…

Q: 5 -5 O 10 X

A: Given that the graph of the circlewe have to find the equation of the circle

Q: Find the intervals on which the graph off is concave upward, the intervals on which the graph off is…

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: f(x) = -3x + 5 g(x) = x² = x² + 2x + 15

A: Given the function   we have to find the value of (gof)(x)

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: Given,a(t)=t+4v(0)= 70=<t=<10

Q: Find f such that f'(x) = 9 √x f(9) = 59.

A: f′(x)=9x,f(9)=59

Q: 6. Find the equation of the line tangent to the following functions ate the given points. a. y = x²…

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Q: sinh(x) = 314

A: sinh⁡(x)=34sinh⁡x=12(ex−e−x)

Q: Vs = ft - f- f+ + f =

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Q: is it 3and -2 for A?

A: A critical point of a function f(x) is a coordinate where the derivative f'(x) =0 for the x…

Q: Find the logarithm. 1 log 5 625

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Q: Determine a definite integral that represents the area of the region enclosed by r = 4. ·b Bounds: a…

A: Given equation of a curve is To find the area enclosed by the given curve

Q: Determine the integral by making the appropriate substitution. √ 2x (x² +17) 3³ dx

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Q: Suppose Find the product AB. AB= Find the product BA. BA= -9 - [3] and 9 A = and B = help (matrices)…

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Q: Find the radius R of convergence for the series R = n=1 2x+1 87+1 n8

A: The given power series .The aim is to find the radius of convergence of the power series.

Q: how that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Four Calculus II students have solved I sin sin(x) cos(x) dx. Their solutions are below. Use what…

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Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

A: The given equation is;2sinxcosx + sqrt(3)sinx=0

Q: Compute the curl ∇ ✕ F of the vector field. F =

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Q: Evaluate the iterated integral. LT (3) (3x - 2y) dy dx

A: we need to evaluate the given double integration.

Q: Find the general solution of the linear nonhomogeneous recurrence relation An = 3an-1 + 10an-2 +…

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Q: 8. The largest angle of a triangle has a measure that is 10 degree less than three times the measure…

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Q: A firm's marginal cost function is MC(q) = 5q¹ + 4q + 10. Find the total cost function if the fixed…

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Q: Let f(x) = x if x ≥ 5 5 if x < 5 a. Find f(1), f(5), and f(7). b. Sketch the graph of y = f(x).

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Q: g. y = tan x h. y = t+√√2t+√1-5t

A: To find the derivative of the following functions.

Q: Write the integral required to find the area of the region pictured below that is bounde 2(y+2) 3…

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Q: 5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

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