2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus rectum (x=2) about the latus rectum.

Q: 3. g(x) = (2x - 1)³

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Q: Complete the following. (a) The graph of y=g(x) is shown. Draw the graph of y=-g(x+1). x 5 ?

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Q: Solve for y at x=2: (4x^3-6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

A: This question can be solved using the concept of differential equation.

Q: Use gauss divergence theorem to calculate the the flow through a surface S that is immersed in a…

A: Concept: The formula for the divergence theorem: ∫∫SF→n^ds…

Q: Two functions and g are defined in the figure below. 8 9 Domain off Range of f Domain of g Range of…

A: Let's solve.

Q: Find the volumes of the solids generated by revolving the region about the given line Use the…

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Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: Solve the differential equation. 7. (cosx cosy – cotx) dx – sinx siny dy = 0

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

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Q: For a battery of voltage V and internal resistance r, the total power delivered to a load with…

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Q: b. S sin (3x) cos¹ (3x) dx

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Q: Perform a first derivative test on the function f(x) = 2x3 + 3x2 - 72x+4; [-4,7]. a. Locate the…

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Q: Find the slope of the tangent line to y = sin x tan (즉) m =√3 2 m = T√√3 3 m = -√3 3 None of the…

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Q: 51 b. Determine the gradient of the following function at Po h(x, y, z) cos xy + e + ln zx, Po(1, 0,…

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Q: 1.y = 5x + 2

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Q: Find the angle θ, in radians, in the given right triangle. The length of the side adjacent to θ is…

A: Given problem:- Find the angle θ, in radians, in the given right triangle. The length of the side…

Q: Find the direction angles of the vector. (Give your answers correct to 3 decimal places.) u = −3i +…

A: Topic = Vector

Q: b. Find the values of dz/8x and dz/dy for the following expression: xe+ ye² + 2 lnx - 2 - 3 ln 2 =…

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Q: b- 2π -50 1 (1+tan²0)3 do

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Q: Verify by Differentiation

A: This question can be solved using the concept of differentiation of function of function.

Q: 5.) Using the tables, evaluate h'(2) for h(x) = - A.) 33√2 C) 33√2 33√2 512 8 33√2 D.) 3√2 f(x) g(x)

A: Given h(x)=f(x)g(x)

Q: 49-7 Estimate lim *-7 -7 is approaching to using a table of functional values.

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Q: VER For a battery of voltage V and internal resistance r, the total power delivered to a load with…

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Q: f(x,y)= exsin (y), fx(x,y)

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Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: 2 61-19]. and C 3 3 Given the matrices A = В: 9 3 5 the matrix X in the equation (A - 5B) X = C. X =…

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Q: A species of bacteria has a population of 250 at 6 a.m. It doubles every 8 h. a) Determine the…

A: Given: Population at 6 a.m =250

Q: mi I Τ 1+ d) √¤√ï√™

A:

Q: Suppose that a product currently sells for $24, with the price increasing at the rate of $5 per…

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Q: A tank contains 100 gallons of brine holding 200 lbs of salt in the solution. Water containing 1…

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Q: Solve for C in the solution for dx/dy = xy^3/(2y^4+x^4) ; y(2)=4 Use 2 decimal places

A: Here we have to solve the given differential equation

Q: There are 28 students in Mr. Connelly's Grade 12 mathematics class. The number of students in the…

A: Denote nA=number of elements in the set.

Q: r3 + y = Ty, then y = 32 3» ყ passos " 1 — 34 + ყ 3.72 O x - 3x² + y 3y² O 32 — y — 3g2 - lf

A: Given

Q: Q1 (a) Using the second shift theorem, find L-1 se s² +91

A: Aaaà

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: We have to check series is convergence or divergence by ratio test

Q: x≤2 Q3. Find the value of k so that f(x)=(x², k-x², x>2 is continuous at x = 2

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Q: ту 3) 2xydy = (x3 +y=) ax

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Q: 2) 2xydy + (x² + y²) dy : > 0

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Q: Use Lagrange multipliers z = f(x, y) = x² - xy + y² to find the absolute maximum and minimum values…

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Q: An unstretched spring is 20 cm in length. If it is stretched to 30 cm, 40 N of force must be…

A: Solved below.

Q: 5. find the derivative 2x (7) + 6x (7) - 2x (²) + 210 Enter your answer

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Q: Solve the differential equation. 12. ( r + sin θ – cos θ) dr + r ( sin θ + cos θ) dθ = 0

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Q: Solve the differential equation. 13. ( sin θ – 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0

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Q: Given that lim f(x) = 9 lim g(x) = -2 lim_h(x) = 0, X→3 X→3 X-3 find the limits, if they exist. (If…

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Q: There are 30 students registered for a multi-sport camp. There are 4 students who will play Hockey…

A: I have appended the formula used in the solution part of the question

Q: sec5 (sin ¹(7x)) √1 - 49x² dx

A:

Q: Pre-Calculus  :  if x=2x=2 is a solution to the equation x^3-4x^2-31x+70 = 0x3−4x2−31x+70=0, find…

A: We have to find out solutions

Q: Answer the questions below about the quadratic function. g(x)= -3x2 -12x -13 Does the function…

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Q: Q1: Solve the following differential equation: 2x² y ; y(1) = 2π y+cos y

A: Explanation of the answer is as follows

Q: 9. 5²-2 dz 10. fdx

A: