If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

Q: Determine the parametric equations of the path of a particle that travels the circle: (x-4)2 +…

A: We have to find the parametric equations.

Q: Given the following information of a triangle, match the missing side or angle with its value. a =…

A: Given the following information of a triangle, match the missing side or angle with its value.a=41…

Q: 3. Find the area bounded on the right by x+y=2, and on the left by y=x and below by x-axis.

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Q: x² + 4x - 4

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Q: 5 (5y, + 1.5y)3 16.036 (5 + 2/3.25y.) INIM

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Q: (b) Determine if the lines are distinct parallel lines. If they are, find an equation of the pla…

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Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: 27t3 dt

A: Given query is to find the integral.

Q: 67 |xsin 3xsin 2xdx

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Q: 00 n=1 5n_1

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Q: Find the most general antiderivative or indefinite integral. dt

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Q: Prove that if A and B are any vectors, then the vectors lBl A + lAl B and lBl A - lAl B are…

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Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) 5zy ze F(1, Y, 2) =

A: Gradient vector field F→(x,y,z) of a function f(x,y,z) is given by,…

Q: f(x) -? The graph of a function f and its tangent line at 0 are shown. What is the value of lim x→0…

A: Given query is to find the limit of the expression.

Q: sec?x - dx |1- 4tan²x 1 –

A: We will solve this question using simple Integration formulae.

Q: Find a solution to the SDE dX = X,(ydX;+ tdt), where y E R is a constant and Xo = 1. %3D

A: This is a problem of differential equation. Based on the variable separation method we will solve…

Q: Find the volume of the region between the cylinder z = 5y and the xy-plane that is bounded by the…

A: To find the volume ..

Q: , If A is an n X n matrix with zeros on the main diagonal then det(A) = 0 Select one: O True O False…

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Q: N. xe S 2(cos x)(sin x)dx = 2 +c (5 In(3x) dx 11. Sln°(3x) o. 12. +C Р. сot x -dx =+c 13. Q. cot?x

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine the absolute extreme values of f(x) = 5x – 10~/x on the interval [0, 16].

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Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: Derive the reductive formula for ∫ ln^n(x) dx

A: Solve using integration by parts.

Q: 5. Figure below shows triangle AOC inscribed in the region cut from the parabola y=x by the line…

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Q: Solve 2logs(Vx)- log;(6x– 1)=0.

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: Find the area under the graph of the function over the interval given. y=x; [1, 5] 2. The area under…

A: Explanation of the answer is as follows

Q: A goat farmer needs to enclose a rectangular field. The area of the field will be 600m^2  The farmer…

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Q: Activity 1.3.2. Consider the function f whose formula is f(x) = 3 – 2x. b. Compute the average rate…

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Q: 6. Find the area bounded by: a. The curve y3D4x-x and the lines y=0, x-1 and x=3. b. The…

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Q: (3 csc² t - 5 sec t tan t) dt

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Q: Current Attempt in Progress Find the value of b for which the differential equation (yeTwy + x) dx +…

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

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Q: 8x, + 4x - X3 = 11 -2x, + 5x, + x3 = 4 2r, - x2 + 6x, = 7 4 %3D

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Q: a A b Note: Triangle may not be drawn to scale. Suppose c = 12 and A = 20 degrees. %3D Find: a = b =…

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Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

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Q: Find the limits as x → 00 and as x → -0o. (If the limit is infinite, enter 'oo' or '-o', as…

A: To find the limits as x→∞ and as x→-∞. If the limit is infinite,to enter '∞' or '-∞', as…

Q: 3. Give a formula for a two-dimensional vector field with both of the following properties: All…

A: 3.Give a formula for a two dimensional vector field with both of the following properties:- Solution…

Q: 1. If we are trying to evaluate thef esinx cos x dx, which substitution would be most helpful? А. и…

A: Select the correct option?

Q: Determine if the following series converge or diverge. If it converges, find its value. n+ n? (a)…

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Q: x2+2x-8 ƒ (x) = x+3 Hole: VA: НА:

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Q: Find the integral (o (b+1)x*2 +(c+1))(x*** +(-1)"(a+2)) dx . b+2c+1 Vx°

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Q: d, 3 Find dx -)- + x(х - 1)). A -3 +2х-1 B +1 -3 +1 -6 +2х-1 x3 (D

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Q: s(D-) dx = Inlxl _6. + C 3 3x. 2 In 3

A: Since the student has posted multiple questions and has mentioned to solve question numbers 6-10,…

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: . What is the outer function? 2. Find dy/du. 3. What is the inner function? 4. Find the derivative…

A: see below the answer and calculation

Q: Use this definition with right endpoints to find an expression for the area under the graph of f as…

A: Here we are asked to use the definition of right end points and get the limit.

Q: Estimate the area under the graph of f(1) = I+ 31 +1 over the interval [-1,2] using five…

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Q: Test differentiability at x = 0 and x 1 for the function x3 + 2x; х — 2; 1 0 <x<1 f(x) = x 2 1 x +…

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Q: Write the limit as a definite Integral on the Interval [a, b], where c, Is any polnt in the Ith…

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