Use an appropriate substitution to show that the value of the following definite integral has value 0 r3n/4 | sin (t) cos(t)dt.

Q: Find dy for the following expressions: dx а) y = x5 In(3x) b) у %3D 2 cos + 2x3 3x2 + 7x + cos (x) y…

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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: Determine the Riemann sum that represents the illustration below. The function is Ax) = /x +1. 4- 3-…

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Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x2 + y? subject to the…

A: Given f(x,y)=x2+y2 and subject to constraint is xy=2 and we need to find the minimum value of given…

Q: 4 Find the arc length of y = (*)* + 70 over [1,2]. 2(x+3)2 (Give an exact answer. Use symbolic…

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Q: The function:  f(x)=2x^3−36x^2+210x−3 has two critical numbers. The smaller one is x= The larger…

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Q: ind the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to…

A: Given problem:- u= 7i+j v=-6i+8j To find:- Angle between vectors in radian and degree

Q: If 11 | f(z)dz 7 70 and 11 g(x)dr = 14 70 and 11 h(r)da = 33 70 what does the following integral…

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Q: dx 3. S- 0 x* + 2x – 3

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Q: The function f is shown below. What is the value of f(x) dx? Write your answer in simplest -5 form.…

A: The detailed solution is mentioned in the step 2

Q: Hwe Find dw and dw for the following functions

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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: Hello, can you please solve the final answer using a right tringle? On there, we are instructed to…

A: After step 3: Line 9:  19-13sin3y+1siny+C We can use the triangle for subtitution.

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: Y2-1 dy

A: Follow the procedure given below.

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2xy

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Q: 1. y=x3 - 6x2 y =0 Answer + 2. y =x4 - 2x y=0 12 -1+

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Q: 5. * 1 dx х (In x)3 1 + C 2 (In x)² 1 + C 3 (In x)2 A C 1 + C 2 (In x)? B D z+C 3 (In x) O A В E…

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Q: Can the Fundamental Theorem of Calculus be used to find 5xcosx?dx?

A: This question can be solved by applying the second part of fundamental theorem of calculus.

Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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Q: 3- use Cramer's rule to solve the system 8x1-4x2+3x3=0 X1+5x2-X3=0 -2x1+6x2+X3=0

A: Here we have to use Cramer's rule to solve the system.  8x1-4x2+3x3=0x1+5x2-x3=0-2x1+6x2+x3=0

Q: ). Determine whether the Mean Value Theorem applies to f(x) 3r + (1,4). -). If so, find the point…

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Q: The lower edge of a mural, 12 feet high, is 6 feet above the observer's eyes. Under the assumption…

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Q: ydx=(ye^y- 2x)dy

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Q: fing the inverR se function of f informally Verify that fleT0) = x and = x+4 5

A: Let f(x) be a given function. Then it's inverse is denoted by f-1(x) such that f(f-1(x))=f-1(f(x))=x

Q: Find the gradient of the function at the given poin w = x tan(y + z), (6, 15, –13) Vw(6, 15, –13) =

A: The given function is w=xtan(y+z) ............................................. (1)  We have to find…

Q: Question Select your answer. Find a number within the interval [-5, 5] such that the sum -5 of the…

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Q: Click an item in the list or group of pictures at the bottom of the problem and, holding the button…

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Q: 3 dx extle) Vx+4 V x+4

A: Explained below

Q: x ys dA X² +1 R.

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Q: 1 Use the geometric series 1 >a* for |æ| < 1, to find a power series representation k=0 for the…

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Q: Which summation notation represents the following series? 1 + 3 + 7 + 15 + 31

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Q: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes. Draw the graph

A: Given query is to find the area bounded by the line.

Q: 4. V21+4:-z dz

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Q: 4y² – 25 -dy

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Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

Q: A farmer plans He needs dimensions would usé the least amount of fence? o equal piece a rectangular…

A: Given:    Area = 194400

Q: Let f(x) = 1² +3xr. Use only the limit definition of the derivative to find f'(2). (Do NOT use rules…

A: f(x)=x2+3x By limit definition…

Q: A rectangular container with an open top is to have a volume of 10 m.. The length of its base is…

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Q: Find the equation of a cosine curve that is obtained by shifting the graph of y = cos(x) - to the…

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Q: 2-use Cramer's rule to solve the system 3tan²x+y=3 2 tan’x -3y=13 X.

A: Given equations, 3tan2x+y=32tan2x-3y=13we know thatfor system  of…

Q: Find all solutions of the equation. 3tan? (0) – 1 = 0

A: The given question can be solved as shown in step2.

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

A: First simplify the integrand then integrate and simplify.

Q: 4) represent the jollowing angles an higono metric cirde a7. + K2n 3. 4. c7 t. Eld

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Q: a) A small metal bar, whose initial temperature was 10° C, is dropped into a large container of…

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Q: Find the principal value of arcsin . 30° 60° no solution

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Q: (1.5)+(-2.3)+(-0.3)+(1.2) + (1,9)? Simplify o= (a) State the answer in square root form and (b)…

A: Given query is to simplify the expression.

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

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Q: y = |x|, y = x² – 1, x = -1, x = 1 - г2 — 1,

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