Consider a solid G, generated by rotating the region bounded by y = 2x² and y = 0 from would the x-axis bounded by CALCULUS x=0 to x=2 through 360° about the x-axis. Sketch the solid G. i) ii) Find the volume of the solid G.

Q: The value of the definite integral 2 [²4x 4x³ dx

A: Given integral ∫12  4x3  dx we use the formula ∫ xn dx=xn+1n+1+C    ; n≠-1

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A: we can complete the table.

Q: c) [ 1: Estimate the area under the graph of f(x) = x² - 1 from x = 1 to x = 3 using four…

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Q: 4. 4 1 [x²ydxdy 20

A: The given double integral is;  x2y, x from 0 to 1, y from 2 to 4.

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A: Given that f'(x)=x-1-2x-2+1 -(i)Also given that f(1)=5.Our Aim is to calculate the antiderivative of…

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Q: Evaluate the following integral. R|N 2 L K|N - 6x sin x dx e *** 2 S (Type an exact answer. Use…

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Q: Find the indicated derivative. 3 If f(x) = 24³x² + 96 3 VX find f'(8).

A: Here we will find f'(8),

Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

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Q: 3x 2. y = Ae³x cos x+Be³x sinx

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Q: Evaluate FR 1.³ 0 sin(2x + 3)dx None of them 0.9989 0.9899 = -0.9899 1.21 -0.9998 -0.9989

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A: Given that fx=3x2-10x+1 at x=3Solution :equation of line in slope intercept…

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: Given f(x)=4x and x=2

Q: The equation represents Select one: x² + y² + z² + 6z = 4x + 12 a sphere with center(-2, 0, 3) and…

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Q: Find the dot product of the following vectors u and 7.

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Q: can you please write it clearly for better un

A: To convert the polar coordinate 5, π4 to Cartesian coordinates.

Q: Let C be the curve y = 12 11 10 9 8 7 16 16 5 A m Cy 1.5 x³ 1 + for 0.6 3.7. 3x 4 2,5 3 Find the arc…

A: We are given a curve C : y= x3/4 + 1/(3x)  for 0.6≤x≤3.7. We have to find arc length of C.…

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Q: In the find and prove of lim”→0 (x³), how and what should be defined in terms of ? A. 8 = min {1, §}…

A: This question is related to Limits, we will solve it using given information.

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Q: 3. fx³√1 + x² dx

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Q: General solution of the differential equation 1-3xy X X X 11 2y 1 2y + 이름 4yy 1 4v ① -) (c) -음

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Q: Find a plane containing the point (-1,-7,-8) and the line of intersection of the plan 6x + 4y + 4z =…

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Q: Q2: solve the differential equation x²y' = y² + xy + x² subjected to the condition y(1)=1 and give…

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Q: Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x)…

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Q: 5. r² = 1

A: As per the rules of the company we can answer only first question and rest can be reposted.

Q: Let a =(4, 1, 5) and 6 = (2, -5,5). Find the angle between the vector (in radians)

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Q: H.W: show that the equations are homogeneous and solve: 1. (x + y)dy + (x−y)dx=0 2. x²dy + (y² -…

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Q: Evaluate 4 2 4 X 13.402 -13.402 13.042 √x + 3 3 X 4 - 4 + 4 + 1 + x)\dx = None of them -13.420…

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Q: Question 11 If sin(0) = 7 and is in the 3rd quadrant, find cos(0) cos(0) = Enter your answer as a…

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P.(0,0,0) in the…

A: Given problem:- find the derivative of the function g(x, y, z) = 3ex cos(yz) ,at the point P0(0,0,0)…

Q: Q4: Show if the series is convergent or divergent cos(n) n√√n n=1

A: Find the limit of the given equation at infinity

Q: 38. The amount of P 20,000 was deposited in a bank earning an interest of 6.5% per annum. Determine…

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Q: Let à (6, 7, 4) and 6=(3,2,2). = (a - b) × (a + b) i

A: To find cross product.

Q: Q5: Find the area shared by the cardioid r = 1 + cose and the circle r = 3 cos 0. Graph the two…

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Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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Q: 4. 4 1 SSx 20 x²ydxdy

A: Topic = Integration

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0,4, -3), and R=(-6, -1, - 5)

A: As we know that; The expression for the area of the triangle PQR is: A=12PQ→×PR→   Given: P=6,-3,-5,…

Q: Given y 2x² find 4.1 The interval(s) on which / increases or decreases. 4.2 The local maxima and…

A: We need to explain function.

Q: Consider the following functions. f₁(x) = 9, f₂(x) = cos2(x), f(x) = sin²(x) g(x) = C₁f₁(x) +…

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Q: The distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: B: e²+² dydx Jo Jo

A: To solve the integral ∫0∞ ∫0∞ ex2+y2dydx

Q: Find the value Saxe-aix dx

A: Given: ∫0∞x e-x10dx

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A: Given: fx=e3x

Q: Q4: Show if the series is convergent or divergent cos(n) n√n n=1

A:

Q: Use the Midpoint Rule with n= 3 to approximate the integral. S √x + 1dx = [Please enter your answer…

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