Rewrite the integrand in terms of u so that the integral f(u) = x √ (32²² -da takes the form (3x²+6)4 ff(u)du.

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A: F=5zcos(x),6zsin(x),2z

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Q: Let f(x, y) = x² + 5y². (a) Find f (3, 1) and f,(3, 1). f(3, 1) = f,(3, 1) - (b) Interpret the…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) [(u² - 346 - U² + ·…

A: Given integral  ∫( u7 - 3u6 - u4 + 63 )du Formula used  ∫xndx = xn+1n+1 + C

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Q: 4. Evaluate and x² + y² ≤ 2. dA where R is the region in the xy-plane for which x 21 (x² + 3²)² R

A: The given integral is: ∫∫R1x2+y22dAwhere R is the region in xy plane for which x≥1 and x2+y2≤2.

Q: The area of a healing wound is given by A = 7². The radius is decreasing at the rate of 2 millimeter…

A: A=pi r2, r=26.

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A: Given, R(3,7) &amp; S(8,-1)

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Q: Use Newton's method to find the roots of the equation: In(a)=4-2. Start with = 3.

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Q: Find all the first order partial derivatives for the following function. f(x, y) = 9x - 5y²-3

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Q: For the function, f(x) = 5x³ - equation of the tangent line at x = 1. 2x²-3x-1, find the

A: given f(x)=5x3-2x2-3x-1→ equation of tangent line of f(x) is,  y=mx+cwhere m is slope of line

Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 9 and with its…

A: Given radius of semi circle ( r ) = 9 Let height of the rectangle = y Given width of the rectangle =…

Q: Find the Maclaurin series of f(x) = 5*. Σ n=0

A: given function fx=5x To Find: Maclaurin Series

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Q: y (5-x) 2 6) Verify Rolle's Theorem on [0,5] for the function f(x)=x√5-x and algebraically determine…

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Q: The graph below is the function f(x) -5-4-2-1 3 -1 -2 Find f(-1) 234 Find lim f(x) 24-1- Find lim…

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Q: Q4.5 Let f be a function completely defined by the graph below on the interval [0, 10]. On the…

A: Please refer to the detailed solution.

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Q: A hot-air balloon is 110 ft above the ground when what is the rate of change of the distance between…

A: Given that , dxdt=44 ft/secdydt=15 ft/secdzdt=?

Q: Evaluate the integral. 1 √2-12 i+testi 2112 (10+7+3)2 dt

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Q: Find the directional derivative of the function f(x, y) = ln(x + y³) at the point (-3, 1) in the…

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Q: 3. A projectile is fired with an initial velocity of 128 ft/s from a cannon at time t = 0 from a…

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Q: Find the order 3 Taylor polynomial T3(x) of the given function. f(x) = (-5x +52). at a = T3(x) = 4.

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Q: he indicated method of solution for the following. Solve: sin x cos² y dx + cos²x dy = 0, y(0) = ㅠ 4…

A: The given differential equation is;  Sinx cos2y dx + cos2x dy = 0, y(0)=pi/4

Q: Find the directional derivative of the function f(z, y) = ln (z+y³) at the point (-3,1) in the…

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Q: 5x² 이 sin (8x) dx = 5 1 xcos(x) + 1 256 (8xsin(x) + cos(8x)) + C

A: We need to integrate: ∫5x2 sin8x dx We can solve this using integral by parts.

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Q: Find √² xdy + ydx, where C is the arc of the curve y = e for 0 ≤ x ≤ 1

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Q: Find a parametric representation for the surface. the part of the plane z = x + 5 that lies inside…

A: Given: The part of the plane  z = x + 5  that lies inside the cylinder  x2 + y2 = 1.

Q: dx 9. ·S 1- x² sin-¹ x Answer -1 In sin¹x +C

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Q: Please solve and show all work. Consider the function f(x) = 2x³-12x²-72x + 7 on the interval [-4,…

A: Given that: The function f(x) = 2x3 - 12 x2 - 72 x + 7  on the interval [ -4, 7]. Average slope: By…

Q: (A) Find the Laplace transform L{f(t)} in terms of s. If f(t) = 8t* + sin(2t) - e-st

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Q: Find the maximum for the profit function, P = 3x + 12y subject to the following constraints. x+y≤ 80…

A: We have to find the maximum profit

Q: Find the area (in sq. units) bounded by the parabolas x²-2y = 0 and +2y-8=0. A. 11.7 B. 4.7 C. 9.7…

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Q: Find the area in the first quadrant bounded by the parabola y² = 4x, x=1&x= 3 A. 9.555

A: To find the area in the first quadrant bounded by the parabola   y2=4x and the lines x=1 &amp;  x=3.…

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Q: Write a chain rule formula for the following derivative. for z = f(r, s); r = g(t), s = h(t) at dz…

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Q: Find the relative extreme values of the function. (Order your answers from smallest to largest x,…

A: The solution is shown in step-2

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A: The total surface area of the box is 5400 cm2

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: Evaluate the following indefinite integral. tan(arccos(3t)) /1 − (3t)² dt = help (formulas)

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Q: Find the limit. (If an answer does not exist, enter DNE.) √x + 2-9 x - 79 lim X→ 79

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Q: A O $5 O $1 O $910 O $10 the Rumber of toys produced. In the long run, what will be the average cost…

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Q: d) Let f be a continuous function. Then 1 [ S f(x,y) dady = f*f* f(x,y) dyda. 0

A: