Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(8y) dy = 0, y( = 8 y(x) = =

Q: f(x)= (4x² +8x+2)

A: We can find the derivative using chain rule as below.

Q: What is the second derivative of the function y = -6 sin x cos x where x is? Round your answer to…

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Q: Find the force on one side of a plate bounded by x = y² and x = 2 - y² which is submerged vertically…

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

Q: Consider the function f(x) = x¹ − 50x² +11, x¹50x² This function has an absolute minimum value equal…

A: We need to find absolute max. and min. value.

Q: Find the length of curve x = t², y = t³ from x = 0 to x = 5.

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Q: A curve is given by the equation x4 + y = 82. Find the equation of the line tangent the curve at…

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Q: ¹ ln(1 + x) dx X 0

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Q: Q1/B) Find the length of the cardioid curve: r = 1+ cose

A: A detailed solution is given below.

Q: The function f(x) 2x³ 33x² + 108x - 6 has two critical numbers. = The smaller one is x = and the…

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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: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: dx (4x²-9)

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Q: 12 [ sin* ‡nxdx

A: We can find the answer as below

Q: f cos4x dx

A: According to guidelines, we must answer only one of the multiple questions given.So I answered only…

Q: 7 dx x4 - 16

A: Given: I=∫7x4-16dx   As we know the common integral. ∫1ax+bdx=1alnax+b+C And ∫11+x2dx=tan-1x+C

Q: Q2: Evaluate the following integrals? 1) [ cos¹x dx 2x dx 2) S (x-2)² (x+2) 3) S: dx

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Q: f(x)= (7x¹-5x-2)

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Q: Cynthia's investment of $81,200.00 in a fund matured to $160,353.29 in 7 years. If the interest in…

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Q: Question x² Find the lower sum for f(x) = 5- on the interval [1, 5] using 4 rectangles. 5 10 F…

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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 dv

A: Let's solve given derivative functions.

Q: Two people on bikes are at the same place. One of the bikers starts riding directly north at a rate…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6…

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Q: 5x Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-₁ 4 (A) 3.667…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ (In(x))²6 dx X

A: topic- indefinite integral

Q: Find the maximum and minimum values of the function g(0) = 56 Minimum value = Maximum value

A: Here we have to find the maximum and minimum values of the function gθ=5θ-8sin(θ) on the interval…

Q: Explain the process and strategies you would use to determine the derivative of y=tanx. Note that…

A: Break the tanx into Sinx/Cosx

Q: Put the equation that is in general form: y = x² + 22x + 112 into standard form: y = (x − h)² + k:…

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Q: 19. x'dx √√5x² +4 -S

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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: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: The growth in the population of a group of rabbits is given by P(t)= 800e0.08t, where P is the…

A: use derivative for finding the instantaneous rate

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) = 2x³ − 42x² + 270x – 4 has two critical numbers. The smaller one is x = and the…

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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: Maple plot + IŅ -6 Given the graph of f (x) above, find the following limits. 16 4- Ņ 0 Ņ 2 4 6

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Q: Use Matlab Commands to solve the following exercises: Excercisel: a= b= Find i. 5a + 2b ii. |3a -…

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Q: Find the absolute maximum and minimum values of the function f(x) = cos²x-3sinx on the interval…

A: Given function, f(x)=cos2(x)-3sin(x) We know that, Suppose that x=c is a critical point of fx then,…

Q: Find f 6x dx?a.x^2+C. b.2x^2+C c.x^2/3+C d.3x^2+C

A: The given integral,        ∫6x dx

Q: Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7, -1,8) lie on…

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Q: Solve for x in the triangle. Round your answer to the nearest tenth. 13 65° x = 0

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Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: If a set S has both a minimum and a maximum, then S is closed.

A:

Q: The atmospheric pressure P(h) (in pounds per square inch) at a height h (in miles) above sea level…

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Q: Suppose that f is a function given by f(x) = 2x + 7. Which is TRUE about the function? ET O None of…

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Q: Consider the function f(x) = 3x² − 2x +9, 0≤ x ≤ 7. The absolute maximum of f(x) (on the given…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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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: R is the region bounded by the functions f(x) = 3x² + 27x + 54 and g(x) = -3²-22-27. Find the area A…

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Q: The derivative of f(x) with respect to x is the function f'(x) and defined as f(x+h)-f(z) f' (z) =…

A: topic- derivative of a function

Q: Question Define R as the region bounded by the functions f(x) = 2x + 1 and g(x) = x + 1 between x =…

A: The functions f(x)=2x+1 and gx=x+1 between x=1 and x=3, the region is revolved about x-axis.