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Q: d'y day + dx5 dx4 y = (C₁+C₂ + С3) ex +C4e²x+C5e-3x y = Cıe2* +Czxe-3x +C3е* + С4е* + С5е* OA) Ō d³…

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Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0, using a vertical element.…

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Q: (1) Determine what comes next in the given pattern and provide solution/explanation: -7,2, 11, 20,.

A: The given pattern,-7,2,11,20,....

Q: Find the equations of the tangent and normal to the curve √√√√y=1 at (9,4) a. Tangent: 3x - 2y = 3;…

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Q: Evaluate the given limit of the following: lim_[Vx2 + x - Vx2 + 4] X+00 Ya

A: Given;  Limx-infinity [sqrt(x2+x) - sqrt(x2+4)]

Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the area of the plane region, 0≤x≤ π²-4 S.U. 4 1.111 s.u. 1 s.u. 2 S.U. bounded by y=sin X. X =…

A: This question can be solved using the concept of area under curves.

Q: Simplify sin(5x) cos(5x) -cot (2x) sin(x cos(x) to an expression involving a single trigonometric…

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Q: TYPEWRITTEN

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Q: Set-up the integral using horizontal element for the area of the plane region, 0≤x≤ bounded by y=sin…

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Q: dx Evaluate ·S= using rationalizing substitution. x1/2 + x2/3 (A) none of the choices B 6 In (x1/6)…

A: The integration of the integral is  1/(x1/2+x1/3).

Q: 8) ff(x)dx; f(x) = 1 + 2cosx, ((²7) x + 1, sxs" TC < x≤ π

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Q: √√2₁ y = ¹, y-axis, y=1&y=3; OY

A: Volume of solid obtained by revolving region around y axis is evaluated.

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: I am attaching image so that you understand each and every step.

Q: Find all critical points of f(x) = 1 + 10x - x² and use the First Derivative Test to determine…

A: We are given f(x) = 1+10x-x2 We have to find critical points of f(x) and using first derivative test…

Q: Let f (a, b, c) = cos (ab) + sin (b) + c where f Evaluate af да 73,7) Option 4 Option 1 π 24√3 T|3…

A: Please see the below picture for detailed solution. None of the given options is correct.

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: The face of a vertical dam has the shape of an isosceles triangle of altitude 4 m with an upper base…

A: I am attaching image so that you understand each and every step.

Q: Find the equation of the bisector of the acute angle formed by the lines 1+2y=3=0 and 2x+y-4=0. 0 a.…

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Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

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Q: Find the area of the plane region bounded by y=-x+2 and y= x2 −2x 7 s.u. 9 S.U. S.U. 9 s.u.

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Q: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

A: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A: Here, the area bounded by the curve f(x)=8-2x2 ; [0,4] is as shown below:

Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: We need to find equation.

Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

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Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: Using Rationalizing Substitution S- O In(y) + C O Arctan(y) + C O2Arctan(y) + C O2ln(y) + C dx…

A: ∫dxxx-1Substitute y=x-1→dydx=12x-1→dx=2x-1dy=2∫1y2+1dy

Q: (5) Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

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Q: Find the area bounded by x2 = 4y + 4 and x = y 2. Using vertical element, what is the integral…

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Q: differentiate y = ln(lntanx)

A: y=ln(lntanx) We know that, ddx(lnx)=1x

Q: Determine the derivative of the following imp of paper, assuming that it is differentiable.

A: given is x+y3=2c(xy4)differentiating both side with respect to xdxdx+dy3dx=d(2c(xy4))dxusing product…

Q: ch among the equation represents the coefficent + 2 = (A + B + C)x² + (−A + B − 2C)x + -A+B-2C = 3…

A: We have to choose the correct option from the given options according to the given information

Q: Set-up the integral using horizontal element for the volume of the solid obtained by rotating the…

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Q: lim (et + t)¹/t t→0+

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: - Find the value of x of which the function f(x) = O a. none of these O b. 1 OC -1 O d. -3 Oe. 3 2-8…

A: Given:f(x)=12x-8

Q: Suppose 0 <m(8)<, and x=2 sec(0). What is the resulting expression if we write √x² - 4 as a…

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Q: The cylindrical shell method is to be used to compute for the volume of the solid generated by…

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Q: The tangent line to the curve at the point (1,2) also passes through d²y the point (-1,4). If at any…

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Q: 2. Evaluate the following by changing the order of integration: L' L 40² a dx dy. 2y

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Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

Q: tank is in a form of a rectangular parallelepiped 5-ft deep, 15-ft wide, and 25-ft long. It is…

A: Given; l=25ft, w=15ft , h=5ft

Q: find dy/dx : y =3√tan3xx2

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Q: d) an = 1 2² +1 ( ² + + - ₁ - ¹ ( ² ) ) n² + 1 2 1² + 1 + + 2 3² +1 + 1 4² +1 + ...

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Q: Given: region R below bounded by the graphs of y = √x - 3, y = 9 - x, and y = 0. /x- (7,2) R (3,0)…

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Q: = log3x + log(5x²-3x) - log3x², express x in terms of y.

A: Topic:- algebra

Q: Find the critical points of f(x) = x³ - 24x² + 144x and use the Second Derivative Test (if possible)…

A: Solution of given question is written in below steps.

Q: A thick cable, 60 ft long and weighing 180 lb, hangs from a winch on a crane. Set-up the integral…

A: To find the work done.

Q: Find the force on one end of a parabolic trough full of water if the depth is 2 feet and the width…

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

A: Follow the procedure given below.

Q: Find the area bounded by x² = 4y + 4 and x = y - 2. Using vertical element, what is the integral…

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