#2. Find the sum of the 8 n=1 1 (3n+ 1)(3n+4)

Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: 4. Let f: [a, b] → R,g: [a, b] → R, and x E [a, b] such that f'(x) and g'(x) exist, g'(x) = 0, f(t)…

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Q: Use power series operations to find the Taylor series at x = 0 for the following function. cos²x…

A: Taylor series of function fx at a is defined as:…

Q: Find the solution of the equation correct to four decimal places. e1+ 4x = 160

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Q: Evaluate the indefinite integral. Select the correct answer. X 64 64 cos(8x) + 64 cos (8 x) + cos(8…

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Q: Given parametric equations and parameter intervals for the motion of a particle in the xy-plane…

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Q: √x dt 1+t² 2 em moves along a coordinate axis al ith velocity v(t) = 2t² -1 meters econd. Find the…

A: Topic:- calculus

Q: 3. Find the volume of the solid of revolution formed by revolving the region bounded by y = x - x³…

A: To find out the volume of revolution.

Q: Use the Limit Comparison Test to determine if the following series converges or diverges. 00 Hint:…

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Q: Find all other zeros of P(x)=x²³ - 7x² + 19x - 13, given that 3 - 27 is a zero. (If there is more…

A: NOTE: Refresh your page if you can't see any equations. . the given zero is so other zero must be

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: Evaluate 3x e +3 5x e 3 dx

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Q: For the following left-endpoint Riemann sum, given Ln as indicated, express the limit as n → ∞o as a…

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Q: Opens left or right Vertex: (-7, 9) Passes through: (-4, 8)

A: Given:   Vertex: (-7, 9)   Passes through: (-4, 8)

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A: Given question:- Identify the extrema of function by recognizing its given form or its form after…

Q: Given the integral below, find the best lower and upper bounds for F that the comparison theorem can…

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Q: Question 9 Find the derivative of y=e^ cos2x, and use it to find the equation of the line tangent to…

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Q: Evaluate the integral Select the correct answer. O ㅇ 12 πC 24 πC 12 + + + 나이 이어 나이 이어 1 4 −|◄ −|+…

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Q: f'(x) = -2 sin(x), ƒ(4) = √² +7

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Q: 12) Find the area Under the curve y = e = from X=0 to

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Q: Consider the following. y = x² y = 12 - x K 16 14 12 -2 10 B 6 4 2 2 8 10 12 (a) Find the area of…

A: To find the area of given region.

Q: (iv) Find the average value of f over the given rectangle. f(x, y) = e³√√x+e", R = [0, 4] × [0, 1].…

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Q: Evaluate the integral. Select the correct answer. O 3100 3100 3100 t + t + sin 16t+sin 32t+C 75 1…

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Q: 7. The value of f √x dx 1+√x A. x-2√x + 2 ln (1 + √√x) + C B. x-2√x -2 1n (1 + √√x) + C C. x-2√x+2…

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Q: For f(x) = 3x4-12x³ + 2 find the following. (A) f'(x) (B) The slope of the graph of fat x = -2 (C)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: try again, answer is incorrect

A: Let's find minimum distance between point and plane.

Q: f(x)=1/(5x+1), a=1.8

A: As we know the Taylor series:  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where centered at x=a.…

Q: A rectangular area adjacent to a river is fenced in; no fence is needed on the river side. The…

A: To find out the dimensions.

Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

A: Given :Function : y=x7andy=x

Q: What is the domain of the following rational expression (include all types of restrictions):…

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Q: 4. Consider the region bounded by y=x² and y=x in the first quadrant. What is the volume of the…

A: Disclaimer: According to the guidelines, the handwritten solutions are not provided at the moment,…

Q: Evaluate the integral [x Select one: O Inx+C O O 3 O None of them O O - 3 X 3 xả ln xdx Inx-+C 3 с 3…

A: Here is the solution:

Q: Let a and b be real numbers. Find all vectors (3,a,b) orthogonal to (6,-8,-7). What are all the…

A: Let a and b be real numbers. To find all vectors 3, a, b orthogonal to 6,-8, -7.

Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

A: Let f(x, y)  be a function of two variables. A pair (a, b) is a critical point of 'f' if either…

Q: x² + x + 72

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Q: O Differentiate Y 2 +1 3/2

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Q: 6. Demonstrate that Σ j=0 1-z' 1-z

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Q: lim x→0 x⁹⁹ sin (7x) (sin x) 100

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Q: Find lim lim h-0 h→0 f(6+h)-f(6) h f(6+h)-f(6) h if f(x)=x² +4. (Simplify your answer.)

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Q: The price-earnings ratio of a stock is given by P R(PE)=E where P is the price of the stock and E is…

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Q: Question 3 (a) (b) Find the area of the region bounded by the curves y = x²(x ≥ 0), y = x² (x ≥ 0)…

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Q: In each of the following cases, find the area of the region that lies inside both the curves. (b)…

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Q: Is (1,1) a unit vector? Explain. Choose the correct answer below. O A. (1,1) is not a unit vector,…

A: We can solve this as follows:

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A: Here we have to choose the correct option.

Q: 7. f sin4xdx

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Q: Determine the solution y2(2) of the differential equation, given that it is satisfied by the…

A: Given :x2y''-xy'+y=0

Q: Find dx X O A. O B. O C. O D. 16 4 **** 5√x 5 X 16 3 X i - 4) - 1x -20% √x - 4√x 5 X 16 3

A: We need to find derivative.

Q: 15. Find the volume of the solid generated by revolving y-axis, the area enclosed by the parabole y²…

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Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

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Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy