Evaluation. Find the antiderivative of the following exponential expression. Show complete solution. 1. f(2e* + 4*) dx 2. f(2-3e*)dx

Q: What is the solution of 3x2 + 6xy2 + (6x2y + 4y2 ) y' = 0

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Q: Perform the indicated operation. Show all work possible. (-4+5i) -(6-9i)

A: a+ib +c+id = (a+c) +i(b+d) a+ib-(c+id) =(a-c) +(b-d)i

Q: Let R be the region enclosed by the curves y = x³ and y = 2x² The area of R using horizontal element…

A: The area of the region R enclosed by the curves, y=x3 and y=2x2 is given by Area=∫cdg(y)dy

Q: Exercise 15.5.1 Evaluate the triple integral * "** (rz sin 0)r dz dr de. =0 Hint 8 X

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Q: 1. csc²x dx 2 4 cotx + cot ³x

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Q: Q.3) +4x+8 dx m a) tan-1/3+2 +c b) in 2 + c c)e()+c d)+c

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Q: 2. Evaluate the double integrals by iteration. whre B is the region 0 ≤ x ≤ 1, ² ≤ y ≤ = Je d.A

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Q: = that pv(x) de d] - f [ra] dx u(x) f (t) ) dt = f (v (x)) v' (x) − f (u (x)) u' (x)

A: Using the definition of the integral and the chain rule in different ion

Q: Let R be & (t) = a vector based function defined loy < 1/2, 1, 0) if t = 1 3-√E 1-t² It cos nt if…

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Q: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

A: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

Q: Show that the points form the vertices of the polygon. isosceles triangle:     (4, −4), (5, 2),…

A: Solve the following

Q: so ne dx

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Q: 9-34 Evaluate the integral, if it exists. tb (1)nia 9. ² (8x³ + 3x²) dx 11. f' (1-x) dx 13. f³√x (x…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first part.

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

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Q: Find the volume of the solid bounded below by the circular paraboloid z = z² + y² and above by the…

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Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

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Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2x = 5 and x-axis.

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: Find derivative of the following function. 7x -7x + e y = X

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Q: 5a) 1 x[In (2x)]3 S.₁- -dx 5b) X ² (x² - 4)" S₁²7 3/2 dx

A: As per guidelines, I can answer only one question. Since both the question are not interrelated. So…

Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

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Q: 2 0 sin 2x dx 3-cos2x

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using horizontal…

A: The given curves are: y=x3 &amp; y=2x2 And A=∫cdgydy    ...1   Now find the point of intersection…

Q: Find the center of mass of a lamina as pictured below, with inner radius 3 and outer radius 5, with…

A: Given problem:-

Q: 1. S √x dx VX +1

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Q: Let z=f(x,y) = 20x² - 25xy + 16y². Find the following using the formal definition of the partial…

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Q: 8. If the slope of the line (k + 1)x + ky − 3 = 0 is -2, find k.

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Q: Trail Rev... = 360 cubic inches. olData Career... A box, with a square base is to have a volume of V…

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Q: Given the graph of the function f(x), answer the following question. B C F D -20 -10 A E -10 Of the…

A: Solution is here

Q: x3 16 + x² dx, x = 4 tan(0)

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Q: Q.22) The integral x-3 dx is convergent if the values of p are: a) (-0,3) b) (-∞, -2) c) (3,00) d)…

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Q: Solve for the homogeneous linear equation given below 1. xydy- (x + 2y)² dy = 0 O-In ()-4lny = C…

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Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write u…

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Q: (A) Find the dimension of a box with A Square base with volume 216 and the minimal Surface area (use…

A: Hello learner, we can answer first question as per the honor policy. Please resubmit other questions…

Q: (e) Every function f defined on (-∞0, ∞) that satisfies the condition that lim f(x) = lim f(x) = ∞o…

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Q: Question 4 (a) An object is moving with position vector r(t) = cos(cot)i+sin(at)j + at³k. (1)…

A: Given :position vector :r(t)=cos(ωt)i+sin(ωt)j+αt2kω=π and α=2 and t=3

Q: sin X SS € y dy dx

A: To evaluate the value of given double integral.

Q: 3. Find the solution of the following systems of differential equatio (c) [x' (t) = -6x (t) + 4y(t)…

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Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

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Q: (a) Identify a suitable method to solve the following first-order differential equation. Find the…

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Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

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Q: -37 :5³T sin³ (1) cos³ (1) dx 0 6

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Q: 3. Find the solution of the following systems of differential equations: (Nonhomogeneous) Use…

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Q: Q5] Find Maclaurin's series f(x) = ev²x.

A: Follow the procedure given below.

Q: (Laplace transform method) حل نمائید. (x) = = - [ (x -tut )dt 6

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: 12. Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

A: Solution: Given lines, y= x +3.....i y= 2x-1.....ii y= -3x+4.....iii By using intersection points of…

Q: Given ; = -5 cos 0 and r₂ = 5+5 cos 0 Sketch and then set up integral for area bounded by the…

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