Use the indicated substitution to evaluate the integral. 2x cos(x) dx , u = x' sin (x²) + C 2 sin (x) +C 2 1 sin (x²) + C 4 cos (x) + C

Q: 3. The chemists say that between 0 C and 30 C, the volume V (in cubic cm) of 1 kg of water at temper...

A: The temperature at which water has minimum volume is T = 3.967°C

Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10...

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the ...

Q: [3 – x2, – 1< x < 2 20. If f(x) discuss its continuity and differentiability. %3D 2x – 4, 2 <x< 4

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Q: Three edges of a right triangular prism are defined by the vectors à= [1, 3, 2], b=[2, 2, 4), and = ...

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Q: x2 dx J V4x – x²

A: Given:       ∫x24x-x2dx    =∫x24-x-22dx  substitute u=x-2→dudx=1→dx=du                    use x2=u+2...

Q: Refer to the figure and find the volume generated by rotating the given region about the specified l...

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Q: 13. Find the solution set of a) |6x – 13x - 5|| = 2x b) 14x 1| > |2x + 3| + 1 c) |2x² – 3x – 4| < 5 ...

A: Discuss all cases and solve it. 

Q: Use a finite sum to estimate the average value of f(x)=x³ on [0,2] by partitioning the interval into...

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

Q: Enclosing the Largest Area The owner of the Rancho Grande has 2,956 yd of fencing with which to encl...

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Q: 4. Vic and Joey argue about the limit of the function f(x)=1/x as x approaches 0. Joey's opinion is ...

A: Claim of Vic is correct, because as per the definition of limit  By evaluating the left hand limit w...

Q: 1000 The logistic growth model P(t)= represents the population (in grams) of a bacterium after t hou...

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Q: Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate ...

A: Let ,Time = t P = $7,000 Rate = 7% = 0.07 P'(t) = dP/dt (a) Write a first-order linear differential ...

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu...

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Q: What trigonometric substitution will you use in solving the below integral? Note: Let W be the angle...

A: Put 8x=15tanw =[12×(15/8)³tan³w]/[5×15√1+tan²w] =(79.10/75)×(sin³w/cos³w)/[sec²w] =1.05sin³w/cos²w

Q: 1. 4x° sec .3 x dx cos Va dx Væ csc Va x2 -dr 2.

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Q: Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the functio...

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Q: a & C

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Q: et dx (9 + e2¤)

A: Integration   by subsitution technique 

Q: DIFTERENTIAL 6QUATO NS Eliminate the arbitraty constans y Iny c,e+ Cze Fihp THe BIFFERENTI EQuntoN F...

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Q: Use integration by parts to evaluate the definite integral. 8t² In(t)dt Give an exact answer

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Q: The function f, shown below, is comprised of a semi-circle and piecewise linear segments. What is th...

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Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find. 

Q: created a mathematical question on inequality( quadratic) and answer the question

A: Inequality is an  expressions that compares the algebraic terms. 

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu...

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Q: Integration by trigonometric integrals/substitution: (4-3 cos (x)) sin²(x)dx

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Q: Use the trapezoidal rule with n = 5 to approximate cos(a) - d.x Keep at least 2 decimal places accur...

A: ∫15cos(x)xdx ; n=5

Q: Given cost and price (demand) functions C(q) = 100q + 43,000 and p(q) = - 2q + 880, what profit can ...

A: Given :cost price (demand) functions C(q)=100q+43000 andp(q)=-2q+880, company earn by selling 50 ite...

Q: 3. Determine whether or not each equation is a function. Justify your answers. a) y =- 2x + 5 b) x? ...

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Q: 12. Solve the following inequalities. a) -7x + 8 < 4x - 2 b) (3- 4x)(x + 1)(7 – 2x) <0 6x-9 c) 3x-2 ...

A: For (a),     -7x+8≤ 4x-2⇒-7x≤ 4x-10⇒-11x≤ -10⇒x≥1011 For (b),     3-4xx+17-2x≤ 0⇒x≤ -1  or  34≤ x≤72

Q: You deposit $2000 in an account with 5% annual compound interest. Complete the following, assuming y...

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Q: 2.2) Solve and explain the steps involved. (2+72)es*dr

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Q: Find the derivative of y = sech ILe-x)

A: Topic:- derivatives

Q: The function f is shown below. What is the value of | f(x) dæ? Writey your answer in simplest form. ...

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Q: Solve each of the following equations for x. log3(x+1) − log3(27) = 2

A: Solve each of the following equations for x. log3(x+1) − log3(27) = 2

Q: Expand (2+V-9) А. 46+9i В. 46-9i С. -46-9i C. D. -46+9i

A: Option (D) correct. For detail go through the solution

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the...

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is ...

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Q: 27 The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) ...

A: Given query is to find the height of the ball when it's fall with the rate of 120 ft/sec.

Q: 2t es the given condition; r' (t) =i+ te-t"j - =k;r(0) = i %3D t2+1 Vt2+4

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Q: Use sigma notation to write the Maclaurin series for the function. 2cosh x (2k)! 2 (2k)! (2k)!" 24+1...

A: Given : f(x) = 2coshx

Q: 27 Given Cost and Revenue functions C(q) = q° - 10q +56q + 5000 and R(q) = - 3q + 2600q, what is the...

A: Let's find. 

Q: 3. x/1+x° 1 dx (use trigonometric substitution)

A: sec2θ -tan2θ =1 ∫cosec(θ) dθ = 12lncos θ-1cos θ+1+C

Q: Solve ſ cot3 4x csc² 4x dx then evaluate the answer at x=22, C=26

A: ∫cot34x csc24x dx

Q: 36) -24i + 32j

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given: So, here an=1317n-1. Now,                limx→∞ 1317x-1=13·limx→∞ 117x-1=13·limx→∞ 1limx→∞ 1...

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: sin x 5 2 0, cos x

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Q: 2. x cosh x? sinh x2 dx

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Q: In getting the derivative of a rational function, just get the derivative of

A: Topic:- derivatives   

Q: Use the trapezoidal rule with n = 5 to approximate %3D 5 cos(x) -d.x 1 Keep at least 2 decimal place...

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