π 元-2 Question 4 (2 pt): Solve the differential equation 3 dy dt - 6t.y = t³ cos 3t, y =

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A: The objective of this question is to calculate the sixth midpoint Riemann sum (M6) for the function…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = In(x² +…

A: Step 1:Step 2: Step 3:Step 4:Comparing the values:ln⁡(11/4)≈1.0116ln⁡(3)≈1.0986ln⁡(23)≈3.1355So, the…

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Q: Consider the vector field F = Evaluate . eF dr along the curve C: #(t) = 3 cos(t); + 3 sin(t)], 0…

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Q: 3a

A: We'll solve this triple integral by integrating it three times sequentially, one variable at a time.…

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A: Step 1:f(a+h)\\ &\Rightarrow f(x)\text{ has a local maximum at }x=a\\ &\text{If…

Q: 2a

A: Step 1:Step 2:Step 3:The change of order gives same answer which is 9.

Q: Consider the ODE dx /+/2y1/2 + y x1/2y/2x Let g(x,y) be that monstrosity on the right-hand side.…

A: Step 1: Given ODE is : dxdy​=x1/2ye/2πxπ/e+xπ/2ey1/2+y​ Step 2: Let the right side of the ODE is:…

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Q: Consider the points A(2,3,7), B(0,3,3), and C(5,2,-4). Find a) The largest angle in triangle Abc…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: (A) Step 1: State the given function and boundaries: f(x)=7x+1a=0b=4 Step 2: Determine the points on…

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A: As x approaches positive infinity, the constant term 14 in the logarithm becomes insignificant…

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A: a. Let's analyze the behavior of (f(t)=et) on the interval (0,0.5) and compare with the Taylor…

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A: Consider,dxd​(ln(x))=x1​dxd​(constant)=0 I hope you have understood the answer, if you have any…

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Q: Find the following limit. lim t 5 answer =

A: Please comment down for any doubt. I hope my answer helps you.

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A: The objective of the question is to calculate the total number of fish required for the experiment.…

Q: Please review the screenshot attached to this request and solve the problem :)

A: Step 1: Step 2: Step 3: Step 4:

Q: part c) and d) please

A: Based on the image you sent, which appears to be a multiple-choice question about the coefficient of…

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Q: 20:31 Till. 26% Tshwane University of Technology We empower people FACULTY OF HUMANITIES DEPARTMENT…

A: QUESTION 1) QUESTION 2) QUESTION 3)

Q: (3) [Marked] Consider the surface of revolution = {(x,y (x, y, z) € R³ | x² + z² *-{\306842-({+1})}…

A: The normal vector from the given plane:

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A: Step 1: To find the equation of the plane passing through the points (3, 0, 1) and (0, 1, -1) and…

Q: Question 9 Difficulty: ill Find the greatest value of y=-2z3+3x² + 12z - 5 in the interval -2

A: Step 1:To find the greatest value of y=−2x3+3x2+12x−5 in the interval −2≤x≤1, we need to find the…

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A: Answer 2)To find the expected population of each country in 2025, we will use the formula for…

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A: Step 1: Step 2: Step 3:

Q: Find the limit. lim x→0+ sin(6x) x4 || 0

A: This limit takes the form "indeterminate" (specifically 00​ ) as x approaches 0 from the positive…

Q: Calculus I May I please have the solution for the following question? Thank you, 7) An industrial…

A: Step 1: Setting up the Area of the tank in terms of the radius of the cylinder Step 2: Find the…

Q: Given f(x, y) = -3x3 + 5xy - 2y5, find fr(x, y) = fy(x, y) =

A: The objective of the question is to find the partial derivative of the function f(x, y) = -3x^3 +…

Q: sin h Use the definition of the derivative and the fact that lim cos(h)-1 =1 and lim = 0 to show…

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Q: (c) n=1 n² + 5

A: The objective of the question is to determine whether the given series converges or diverges. The…

Q: 0 find max/min: • f(x) = 3x²+4x=6 • 2 find intervals af. cancavity. • f ( x ) = 8 × ² ( 4x + 3 ) .

A: Step 1:Step 2: Step 3: Step 4:

Q: Use Newton's method to approximate a root of the equation 5׳ + 6x +3 = 0 as follows. Let x1 = −2 be…

A: Step 1: Step 2: Step 3: Step 4:

Q: Please review the screenshot attached to this request and solve the problem :)

A: Step 1:​f(x,y)=2x2−x4+3y2​Step 2:​Using the Power…

Q: Consider the function f(x) = 4√√+7 on the interval [3, 7]. Find the average or mean slope of the…

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Q: Use the Midpoint Rule with n = 5 to approximate the area of the region bounded by the graph of f and…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: The objective of this question is to find the absolute maximum and minimum values of the function…

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A: Step 1: To find the slope of the function and check the inflection points, we need to follow these…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. '5 1³ ex ex sin(x) dx…

A: If you have any questions let me know in comment box thankyou for your question.

Q: 2) Change the order of integration for the triple integral (x² + In(y) + z)dx dy dz so that you are…

A: The objective of this question is to change the order of integration for the given triple integral…

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Q: 3) Evaluate the triple integral f₁₁₁³ (ze* +2y) dx dy dz. Give answer exactly.

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A: Step 1:       Step 2: Step 3: Step 4:

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Q: 8 Ay 10- Compute the following estimate of f(x) dx using 0 8- y= f(x) the graph in the figure. 6-…

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Q: Find the largest value of the function f(x) = x³ — 4x² – 10x + 5 - - on the domain -6≤ x ≤ 6.

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Q: please help solve and explain

A: Step 1: