O By direct partial integration, Solve the following PDES 8- аги axdy = CBX COSy? SXUCX,t) Ex u(x₂) = x, U(#₂ y) = 2 cosy 2 2 Ans: u(x,y) = sinx siny + 1/² + 2 cosy - #2² ♥

Q: 3. Test the following series for being convergent or divergent: (2) Σ < (3n)! n!(+1)!(+2)! (c) Σ…

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A: We will use basic logarithm properties.

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Q: 3. Use a known Maclaurin series to obtain the Maclaurin series for the following. f(x) = = x COS…

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A: Integration by parts : ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx

Q: Given the function f(x) = 5x(sin x + cosa) what is f' (4)? O No correct answer O -1.996 O -2.99 Ⓒ…

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Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: The function f(x) Find it. X = = (4x4)e5 has one critical number.

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Q: Every set S has an open cover.

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

Q: Evaluate Sc (4x+3√7) ds ds where C is given in the accompanying figure. Sc (4x + 3√/y) ds = (Type an…

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Q: 20. √9-5x² X -dx

A: SOLUTION-

Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: Consider the solutions Y(t) of with a, b, d constants and a, b>0. Calculate lim y(t). t-x Hint:…

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

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Q: If f(x) = 5x(sin x + cos x), what is f'(x)?

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Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: The given indefinite integral is: I=∫dx4x+3   ...1   As we know the common integral. ∫1xdx=lnx+C

Q: [Select] A. f(x) = 3x² + 2 B. f(x) = 3x² +4 C. f(x) = 4x³ D. f(x) = 3x4 [Select] A. 6 B. 5 C. 3 D. 2…

A: topic- functions and limits

Q: Solve the equation to find the value of a,b,c and d. Eqn 1: 6 = 6 b + d Eqn 2: 6 + 4 = 3b + c +…

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Q: 22. CHALLENGE If rectangle ABCD has coordinates A(0, 0), B(0, 4), C(4, 3), D(0, 3), find the…

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Q: What is the derivative of −9 sin² (-3x³)? O-162x³ sin (-3x³) cos (-3x³) no correct answer O 162x²…

A: just differentiate the given function by using chain rule of derivative and easily find the required…

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Q: Change the Cartesian integral to polar coordinate dy dx 171-72 حول من كا الا بولير -1 0

A: ∫-11∫01-x2dydxIn polar co-ordinates, Let  x = r cosθ    and    y= r sinθThen , r2 = x2+y2     and…

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A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Prove using the properties of set operations: a. If A and B are sets then [(A - B)c n A] C B

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Q: 1. S 2. [x²e²² dx 3. [sec* (x) dx 4. fxinx dx 5 ( x50x² dv x arccos x dx 6. Jese² (3x) dx 7. fx³ež…

A: Since multiple questions are asked, I am answering first question

Q: Consider the function f(x) = 4 − 4x², −5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x…

A: Consider the function fx=4-4x2, -5≤x≤1.To determine the absolute maximum and the absolute minimum…

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Q: 1. y=-x²-3x+6, x+y−3=0; about y = 0

A: First, we graph the given equations using a graphing calculator.  The shaded region is rotating…

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Q: Directions: Find the area of the region bounded by the curves. Use a clean sheet of paper for your…

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Q: QUESTION 2 Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

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Q: ou are given the polar curve r = cos(0) + sin(0). a) List all of the points (r, 0) where the tangent…

A: Let's solve. Given polar curve equation.

Q: Which of the following is a point on the plane with equation n = (-3, -2, 2) + t(2, 2, -2) + s(1,…

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Q: What is the second derivative of the function y = -7 sin x cos x where x is ? Round your answer to…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We can solve this as follows:

Q: Which equation shows the correct derivative of the equation y = 2x² + 16x +3?

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Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

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Q: [Select] 3x²+3 ³+3x-4 3x² +3 In{³+3-4} 1 ³+30-4 1 In{³+3x-4} 32-4) A. f'(2) 6.51 B. f'(2) = 1.5 C.…

A: Given function is  f(x) = ln(x3 +3x-4)  20) find derivative of f i.e. f'  22) find f'(2)

Q: ¹In(1+x) -dx 0 X

A: Expand log series

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (1,4,5)…

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Q: Use the arc length formula, L = √√√1 + (f' (x))² dæ, to find the length of y = 2ª + 1 on [1, 5].…

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Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A: Please refer to the image below