Use the Fundamental Theorem of Calculus to find the derivative of the following function 5 F(x) = [² X cos t -dt

Q: (5) If f(x) = sin (22), which of the following is true? (A) There is a local minimum at z = 0 (B)…

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Q: Suppose that f(4) = 6 and f(9) = 7. Which of the following statements must be true? (i) If f(x) is…

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Q: Find the value without finding the antiderivative. 5 [²√ 25 - X² dx

A: To find the value of the following integral without finding the antiderivative.

Q: Use logarithmic notation to represent the solution to each of the following equations. If there is…

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Q: 49. Sigma notation Evaluate the following expressions. 10 Σκ k k=1 6 b. Σ (2k + 1) k=1 4 a. C. k2…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: The position function for a particle's motion on a line is s(t) = t³ -t²-t + 1, t≥ 0, s is in meters…

A: The position function for a particle is .The aim is to find the time  for which the particle is at…

Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), E is bounded by four planes: z = 0, x=0, 2 3…

A: Volume of tetrahedron

Q: Click on the graph to view a larger graph Use the Law of Cosines to find the indicated angle a given…

A: given triangle ABC

Q: Draw a graph of the signed area represented by the integral and compute it using geometry. '3 L₁₁x1…

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Q: Find the absolute maximum and absolute minimum values of f(x) = [-5,5]. 1. Find the absolute maximum…

A: To find the absolute maximum and absolute minimum values of  on the interval .

Q: True or false: If f is a differentiable function, then [ƒ(√)] = d dx f'(x) 2√x

A: To determine whether the following statement is true or false.If  is a differentiable function, then…

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder a2 + y2 = 25 and…

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Q: A theater charges $70 per ticket for seats in Section A, $50 per ticket for seats in Section B, and…

A: A theater charges $70 per ticket for seats in Section 4, $50 per ticket for seats in Section B, and…

Q: (7) Find the local linear approximation of f(x) = √2+3 at zo = and use it to estimate the val of…

A: The linear approximation of function f(x) at  is The given function is

Q: Consider the function f(x)= xe 5, 0≤x≤ 2. This function has an absolute minimum value equal to: 0…

A: We use the concept of maxima and minima to find the maximum and minimum values of the given…

Q: g(b) Use the substitution formula [f(g(x))g'(x)dx= [ f(u)du where g(x) = u, to evaluate the…

A: By using substitution method, we will find the integration.

Q: 4. Solve the following inequality. Write the answer in interval notation. (x + 5) (x - 3)²(4x +3) >…

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Q: The function f(t)=6900(0.993)^((t)/(12)) represents the change in a quantity over t months. What…

A: The function f(t)=6900(0.993)^((t)/(12)) represents the change in a quantity over t months.

Q: Assume the point (5,7) is on the graph of y=f(x). Determine the value of n in the following…

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Q: Find the total area of the shaded region bounded by the following curves. x= 12y²-12y³ x=2y²-2y

A: From the given graphRegion is bounded by x=12y2−12y3 and x=2y2−2yFrom the…

Q: Substitution in the Definite Integral S Suppose we want to evaluate the definite integral, H -6…

A: ∫3 5 (- 6) / (9x + 6) 2 dxWe make the substitution u = 9x + 6 As beforedu = (du/dx) dxAnd so, with u…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [xe 3x…

A: Green's theorem:

Q: $8000 is invested in an account that pays interest of 3% compounded daily. What will the account be…

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Q: a. What is the solution to the equation 4* x = the number that is X = b. The solution in part (a)…

A: To solve the following equations.

Q: 5 Evaluate f de using the Fundamental Theorem of Calculus, Part 2. Use exact answers only. Use…

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Q: For the function f(x, y) = x^2 + kxy + y^2 where k is a constant, determine if f(x, y) has any…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Sc cos…

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Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

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Q: Obtain general solution. 1) y''-y=ex-4

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Q: Consider the following. √² √√√√²x-x² 8√x² + y²dydx. (a) Convert the iterated integral to polar…

A: Given the integration                                                                  then we have…

Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

A: Here, a  rectangular  Norman window is given having a semicircular top on it.Now,

Q: b. f(0) = f "(0) = sin 0 + cos 0, f(0) = 4, f'(0) = 1

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Q: I ||

A: Given the picture of the trianglewe have to find the value of x

Q: a. Identify the coordinates of any local and absolute extreme points and inflection points. b.…

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: (8) Find the differential for the function using logarithmic differentiation. y = (sin x) (sec): dy…

A: The given function is .The aim is to find the differential for the given function.Formula used:

Q: Given: (x is number of items) Demand function: d(x) = 588.7 — 0.2x² Supply function: s(x) = 0.5x²…

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Q: 4. I-¹ 2 s² 4 (s + 1)ª

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

Q: Suppose that the position functions of two particles, P₁ and P₂ in motion along the same line are 1…

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Q: (7) Find the local linear approximation of f(x) = √2+3 at ro = - and use it to estimate the value of…

A: f(x)=1/sqrt(2x+3), x0=-1

Q: Ornithologists have determined that some species of birds tend to avoid flights over large bodies of…

A: Given AB = 3km,BD = 10km.

Q: Find the relative rate of change of f(x) = 12 +2e-2x The relative rate of change of f(x) is

A: The objective of this question is to find the relative rate of change of the function f(x) = 12 +…

Q: i would like to know how to calculate this without a calculator or big numbers

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Q: a. Determine, without graphing, whether the function has a minimum value or a maximum val b. Find…

A: f(x)=3x2-30x-3

Q: Consider the function the f(x) = x¹(4 − x)³. (a) Find all critical numbers of f(x). (b) Find the…

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Q: 5. Use the method of linear system (the Gaussian-elimination method) to determine whether the…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: a. limx→4 x² + x +4 b. limx→-3 2 h² +4h+3 h+3

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Q: Consider the given limits (a is a constant). lim f(x) = 0 lim g(x) = 0 D+X limp (x) = ∞ limq (x) = ∞…

A: Here we have, limx→af(x)=0limx→ag(x)=0limx→ah(x)=1limx→ap(x)=∞limx→aq(x)=∞

Q: Given: (x is number of items) Demand function: d(x) 4563 √x Supply function: s(x) = 3√x = Find the…

A: For equilibrium quantity of the demand function, d(x) and the supply function, s(x) is when…

Q: For Exercises below, solve for the angle 0, where 0 ≤ 0 ≤ 2π. 38. sin² 0 = =1/44 39. sin 20 cos 0 =…

A: we need to solve the given questions and find the solution angle