) Approximate ſ*^*In(y +1)dy with a midpoint Riemann sum using three equal subintervals. 1

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Q: 4) A manufacturer has determined that the total cost C of operating a factory is C = 0.5x^2 + 15x +…

A: Given, total cost C of operating a factory is C = 0.5x^2 + 15x + 5000  where x is the number of…

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A: If S is a subset of  R,   Then every set S  will always have an open cover.

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A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

Q: EXAMPLE: (0,0) 3x-2y 26 5x+45 O > 5 x a 1915 CRITICAL POINTS -A (30) ( B (2.0) 1 D ( ¾/5,9). ✓c…

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Q: Consider the function f(x) = 3 - 3x², − 4 ≤ x ≤ 1. The absolute maximum value is and this occurs at…

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A: Let's find volume of solid bounded by curve and plane by using double integration.

Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, t€ (-∞0, +∞0).…

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Q: Deon's shirt is 4 times larger than Helen's, but costs half as much. Deon's shirt cost $9.35. How…

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Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

Q: O C. Z= (sin O D. Z= (cos + i cos Write the complex number 9-9√3 i in exponential form. z= (Simplify…

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Q: A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as…

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Q: ¹In(1 + x) -dx X

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Q: A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 114 ft/sec Not…

A: Given problem:- A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.…

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Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: Question 12 ( What is the function of cos that has an amplitude of 4 a period of at (0,2)? and has a…

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Q: Find the solution of the given initial value problem. 9 cos t y' y = y(π) = 0, t-9, t> 0 y(t) = =

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Q: - show that V(x,y) = x 'f (2x+y)

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Q: Round-off your final answer to two decimal places 5. √3x + 4dr

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Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: 11. Oil is being pumped continuously from a Texas oil well at a rate proportional to the amount of…

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Q: √x + 1 / dx X (Hint: Let x + 1 = u².)

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Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

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Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it da da d. +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: Given

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A: given

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

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Q: 4. Evaluate the double integral: y f. L y¹/3 x7 +1 (Hint: Change the order of integration to dy dr.)…

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Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

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Q: Let f be defined at all real values of x and x = -3 is one of its critical numbers. If f" (x) = 2x +…

A: Given, f is defined at all real values of x. x=-3 is one of the critical points. f"(x)=2x+1

Q: Q1/ Solve the initial value problem (IVP) of the differential equation by using the appropriate…

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A: Given

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A: Given the plate is bounded by x = y2 and x = 2 - y2 and the plate is vertically submerged such that…

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Q: If s(t) 813 122-48t6, where t2 0 represent the position of a particle traveling along a horizontal…

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Q: Using the substitution u = x - 1, we get the following. (Remember to use absolute values where…

A: ∫1x-1dx=∫1udu                 =logu+c ∫1x-1dx=log(x-1)+C

Q: show that V(x,y) = x 'f (2x+y) is the general Solution of 9 dv X du 2x = V dx 1 ay

A: Given: V(x, y)=xf(2x+y) Find: the general solution of Xdv/dx - 2XdV/dy= V

Q: Solve the given differential equation. All solutions should be found. dy e5x+10y = e dx NOTE: Use c…

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A: We have to find the population.