sin 2x dx Evaluate the definite integral: COS X

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt when  r=2.

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Q: cos³x dx sin*x

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 1. y sinx – xy² = c -

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Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

Q: 2. What is the slope of the line tangent to the curve 8x³ – y² = 4 at the point (1,-2)? 3. What is…

A: Since first subparts question statement missed. Answer 2 and 3

Q: Evaluate the integral below by interpreting y=(x) it in terms of areas in the figure, A1 A3 The…

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Q: x ys dA X² +1 R.

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question is based on 3d line equation.

Q: g (x) .5 Compute g(1) + g' (1) + g" (1) + g" (1) + g'

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Q: Direction: Find the differential equation of the family of curves described. 4. Ellipse with center…

A: Equation of ellipse is x^2/a^2 + y^2/b^2 = 1

Q: Direction: Solve the following equations using separation of variables. 3. 2xy + 6x(x² – 4)y' = 0…

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Q: 1-cosx The value of limx→ by using series is 0 sinx True False

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Q: ................................................. Determine whether the lines intersect, and if so,…

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Q: Solve for the following application of first order differential equations. Show your solutions. 5. A…

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Q: f(b) – f(a) Find the value(s) of c that satisfy the equation = f'(c) in the conclusion of the mean…

A: We can find the value of c that satisfy the equation  f(b)-f(a)b-a = f'(c) .

Q: The thermometer reading 700F is placed in an oven preheated to a constant temperature. After 1⁄2…

A: Given problem:- The thermometer reading 700F is placed in an oven preheated to a constant…

Q: 2. Consider the graph shown on the right. a) What is the minimum and the maximum value? b) What is…

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Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra

Q: Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and the…

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Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: Q.3 Find general solution by separating the variables. i. y3 = (y* + 1) cos x dx. ii. y' = 3x²(y² +…

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Q: dm 1-n3 Find if m = 4 In dn 1+n3 dm n6-1 dm 12n2 %3D dn 12n2 dn 1-n6 Option 4 Option 1 dm 12n2 dm…

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Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

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

Q: 1- use Gauss Elimination to solve the following set of equations: 3x-y+z=-2 x+5y+2z=6 2x+3y+z=0

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Q: Consider the function: f(x)=10√x+8 on the interval [1,8] .Find the average or mean slope of the…

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Q: Use the series representation for cos x, cos x = 1 – + to find the following three items: 6! 1- A…

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Q: 1 EVA LUATE ECs) OF THE DIFF ARD 4(0)-0. dy dt² dt

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Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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Q: d. x cosy + y sin x –1 = 0 3 х е. = 2 x y

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Q: The graph shown below is f(x) = 2 cos x. If g(x) = Sřf(t)dt , find g '( 1 ). %3D 4 3- 2- 54 3 2 -1 1…

A: Use the Newton Leibniz Theorem and calculate the derivative.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: 5. * 1 dx x (In x)3 A 1 + C 2 (In x)² C 1 + C 3 (In x)² 1 + C 2 (In x)2 1 + C 3 (Inx) - - O A O B O…

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Q: ) If we apply Rolle's Theorem to the function f(x)=2x^2−8x−4 on the interval [0,4], how many values…

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Q: A ball is thrown vertically upward. Its height h feet after t seconds is given by the formula…

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Q: If f(r)dr = f(x)dr+ | f(z)dr - f(r)dr. 7. what are the bounds of integration for the first integral?…

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Q: Evaluate by separation of variables. dß %3D и(1 — и?) sec? р du 2 tan B+ sin 2ß = C – (1 – u?)? 2u?…

A: To solve the given differential equation.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Evaluate the following IMPROPER INTEGRALS. It is optional to double check your answers/solution for…

A: To evaluate the given integral.

Q: Which of the following integrals are improper? (Select all that apply.) dr 6x – 1 dr 2r – 1 sin (x)…

A: An improper integral is an integral that has either or both limits infinite or the integrand reaches…

Q: Answer the following True or False. If f(x)dx 0 and f(x) is continuous, then a = b. O True O False

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Q: 6. Find the area of the region enclosed by the graphs of y = Vx+1 and y = }x – 2 and the vertical…

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Q: Find the exact average value fave of f(r)= V16 [0,4] where f(c) = fave- - Iʻ between 0 and 4, then…

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Q: /Factored) Evaluat the indefinite Integral. Write your answer in xp गके एके +उमणेप्याउ 1- et:

A: To evaluate: I=∫x+2-1dx

Q: 3. x'sec'ydy - (1– 2x'tany)dx = 0

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