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Q: Let g(x) = ² + 12 Ax² + B (x²+12) C A = B = C= = D = E = F = g"(x) = x(x² + E), where (+²+F)G where…

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Q: he graph of the derivative g' has exactly two roots. Complete parts a through c. OB. There are no…

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Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: Consider the following. {-x³ +3, -x² + 4x, x≤0 x > 0 Find the critical numbers. (Hint: Check for…

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Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to write the given function as a composition of two functions.

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Find the solution of the following problem. y' - (x + y)(x + y +3) = 1

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Q: Let A(x) = f(t)dt, with f(x) shown in the graph below. 4 3 2 1 X -1 -2 -3 -4 -5 A 5 At what x values…

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Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: Find the derivative of the function. g(0) = (cos(70))4 g'(0) = || X

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Q: Use the given information to find f '(5). f(x) = g(x)h(x) g(5) = -1 and g'(5) = -4 h(5) = 8 and…

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Q: Complete the table. y = f(g(x)) y = (6x - 1)4 u = Need Help? Read It u = g(x) y = f(u) =

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Q: Consider the function F(x, y) = xy2 + 2xy-6y2-8x-12 y + 54. (a) Find the critical points, where Fx…

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Q: Suppose that an airplane flies along the path r₁(t) = (2t, 2t², 10e-t) and a skydiver takes the path…

A: Given that the an airplane flies along the path  and skydiver takes the path  for

Q: a. b. C. Find the derivative of the function. y = sin(tan(7x)) Find the derivative of the function.…

A: According to Bartleby answering guidelines, we can answer only first three subparts. Kindly post…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. √20 maximum value…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: (c) Part of the graph of g(x) = x + x² is given below. Use calculus and algebra to find all possible…

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Q: Consider the function f(x, y) = (4x-x²) (2y - y²). Find and classify all critical points of the…

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Q: log(x2+x+ ex cos(x)²) log(log(log(x)))

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (15 tan…

A: y=limθ→π2−(15tan⁡θ)15cos⁡θ

Q: (b) Isolate дет 11 2x 5 = 1/2gt²2² + vt

A: To isolate  in the following equation.

Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: Find the square root of 7225 with the modern method

A: A number's square root is a value that, when multiplied by itself, returns the original number.

Q: Given the graph of f(x) shown, sketch the graph of the function described. y=f(x+4) Which of the…

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Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: SS (3X-5) dA; R is R Eval & Reverse ? Triangular Region bounded b y=x+5 Y=-X+7 X=10

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Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

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Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: Differentiate the function. f(x) = √√In x f'(x) =

A: Given

Q: For this interval notation, draw its graph and write its equality: (-∞0, 6]

A: The given interval is .The aim is to sketch the interval and write its equality.

Q: Find the limit if it exists. lim (5x+8) x→-5 Select the correct choice below and, if necessary, fill…

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Q: 5). Find the power series solution to y" + xy = 0, y(0) = 1, y'(0) = 0.

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Q: List the first five terms of the sequence. a1 = 2, : 2, a n + 1 an + 1 = 2an + 4 21 2 а2 8 12 14 16…

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Q: Let f(x) = 5 − 3x²2 and g(x) = x + 5. Compute the following. (a) (fog)(x) (b) (c) (e) (fog)(-1)…

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Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: an = 2n + 5 245) 4n+1

A: First, let's consider the limit of the sequence as n approaches…

Q: Evaluate the definite integral by interpreting it in terms of areas. 7 (3x - 18)dx 3

A: To evaluate the following definite integral by interpreting  in terms of areas.

Q: Find dy dx In (y²) = 4x + 5 - dy dx dy dx dy dx dy dx = = - = 2y -2y 2 K|N Y 2 У

A: Given.ln(y²) = 4x + 5

Q: Find the general and particular solution of the O.D.E. y' = (y + 4x)², subject to y(0) = 1, by first…

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Q: List the first five terms of the sequence. an 1 + an a1 a2 аз a4 a5 || = = = a₁ = 6₁ an+1 =

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Q: 23-28 (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

A: (a) To find the intervals on which f is increasing or decreasing, we need to analyze the derivative…

Q: A volume is described as follows: 1. the base is the region bounded by x = -3 =-y² + 4y + 66 and x =…

A: The base of the solid is bounded by the curves:The intersection points of the curves:Hence, the…

Q: Solve the following non-homogeneous differential equations: x" (t) + x(t) = 2 cost 1) -X 2) y"+2y+y…

A: The given differential equation is; x2y''-2xy'+2y=xlnx

Q: Let g(x) = 2x² - 216x. Find the relative maximum and minimum values of g. Also find the intervals on…

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Q: 1. a = (2, 5, −4), b = (1, −2, −3) 2. a = (-1,0, 2), b = (3, 4, −5)

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Q: Find the derivative of the algebraic function. c5-x5 c5 + x5 f'(x) = f(x) = c is a constant. X

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