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Q: 3 Sx³ e³x² dx

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Q: Given two functions F and G, we say that F is an antiderivative of G when O F'(x) = G(x) for all a…

A: Above two questions are answered.

Q: Evaluate the following limits. 1 - cosh x 1. lim x+0+ ln(x² + 1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A:

Q: | (sinh x)(coth’x + csch3x)

A: The solution is given in the next step.

Q: e same overtime Create Workflow xb₂) 5(21 @ (1) The volume of the solid obtained by rotating the…

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Q: Find the Integrating Factor (I.F) of the following linear differential equation:

A: Please refer to the image below

Q: 1. Let B = {. What is A. C. B. ( D. cannot identify } and the operation * is defined by the table…

A: To find what element we get after operating the given elements.

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y 0, and x = 49 is…

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Q: Whatis the equation of the line that passes through (-3,5) and is parallel to theline 4x - 2y + 2 =…

A: The line passing through -3,5 and parallel to the line 4x-2y+2=0

Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: Topic:- application of integration

Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: 3 foa 0 (|3x − 1| + |3* – 3|) dx

A: Use integral concept

Q: Evaluate the indefinite integral given below. (10 (10-20x4) csc² (2x³ - 5x) dx

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Q: The population of a municipality in the country varies according to the function…

A: Topic:- Algebra

Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

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Q: 4. Swin (w - 2) dw

A: The given integral is: I=∫wlnw-2dw   Apply the integration by parts to solve the above integral.…

Q: equences . Given that a₂ = 6 and as 96 are terms of a geometric sequence, find a. 2. Given that a10…

A: solution

Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

A: To find for what  values of r the given term becomes solution of differential equation.

Q: (a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: x≤ 1,0 ≤ y ≤ √1-x²,…

A:

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: Define R as the region bounded by the graphs of f(x) = 2√x and g(x) = over the interval [0, 1].…

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Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: Q1/ Without using L'Hopital rule, find the following limit. √2+x-√2-x lim- ×-0

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Q: 2. (² (sin³x)√1+cos x dx

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Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: 0 sinx + 2cosx dx

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

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Q: 4x Find the average value of the function f(x): - 5 Submit your answer as an exact value. Provide…

A: Given problem:- Find the average value of the function f(x) =(4x/5) + 1 over the interval [-1,3].

Q: I. Evaluate the following limits 2. lim (3 + x)² x → +∞o

A: Given

Q: 10. Consider the function f(x)=2x^2 +(0.4)x If the constant of integration is C=7.2, what is the…

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Q: Evaluate fsin² 2xdx Show step-by-step solution.

A: We need to do integration of  sin2(2x)  First we will apply it's formula, since this value is equal…

Q: Evaluate the integral: 3 So |2 - 2x| dx

A: Given,∫032-2xdx

Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…

Q: Answer

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Q: Evaluate the following: 4 fsin 2xcos²2xdx

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: II. Evaluate the following integrals. fe (sin³x)√1 + cos x dx 2.

A: ∫π/2πsin3x1+cosxdx sin3x=sinx(sin2x)=sinx(1-cos2x) ∫π/2π(1-cos2x)(1+cosx)sinxdx let 1+cosx=t…

Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: S √x²-25 dx X

A:

Q: What is the center of gravity of the solid formed when the plane region bounded by 2x + y -2= 0, y =…

A: The given region is as follows: Now, rotation of the bounded region about y-axis will result in a…

Q: lim (sech 2x)csch x x² +0+*

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A:

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: (x + tan y) dy = sin 2y dx

A:

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: II. Evaluate the following integrals 3. S 3* sech³ (3¹) -dx 1+tanh (35)

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Q: ng a trig substitation, the integral (A) / sec(0) do dr can be transformed into one of the

A: Please refer to the image below