Evaluate the definite integral D= D = = 1/3 cos(πw) dw. NOTE: Use exact values only. Do not provide a decimal approximation for your answer.

Q: Suppose that f' (3) = 0 and f" (3) < 0. Which of the following must occur at x = 3? (a) an…

A: we need to find out the correct option.

Q: Find the area of the region bounded by the line y = 4x, the curve y = Area = √405 x and the x-axis.

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Q: D.f'(x) is decreasing at x = | I E. The slope of f(x) is positive at x = F. The slope of f'(x) is…

A: We know f'(x) decreasing when f''(x)&lt;0 The slope of f(x) positive when f'(x)&gt;0 The slope of…

Q: Evaluate the integral dx (6x + 9) ³¹ by making the appropriate substitution: U= f dx (6x + 9)³

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Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. y² = -16x

A: Given Equation:- y2=-16x

Q: A flat metal plate is mounted on a coordinate plane. The temperature of the plate, in degrees…

A: Solve the following

Q: 2. y = -2 cos(2x)

A: To sketch the graph for one period and to to determine the amplitude and period for the following…

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Find the slope of the tangent line to: a The parabola y² = 6x at the point (3,2). b The ellipse y² +…

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Q: tan¹y-sin y y' cos y lim-

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Q: 3. Graph the function =) lim f(x) x-1 Evaluate. If the value does not exist, explain why. a) lim…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 1. Convert each of the following radians to degrees and sketch the angle measure: a. π/6 b. π/4 C.…

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Q: Find the double integral by changing to polar coordinates. (Express numbers in exact form. Use…

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Q: Consider the function f(x) = 3 x3 27 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

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Q: Differentiate implicitly 14. 4√x – 8√y = 6y²

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Q: The 17th term of an A.P. exceeds its 10th term by 7. Find the common difference. Show that 2√3-1 is…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: a. Determine whether the Mean Value Theorem applies to the function f(x) = ex on the given interval…

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Q: = 2+ sint, y = 1+3 cost. For what values of

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Q: Use trigonometric identities and algebraic methods, as necessary, to solve the following…

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Q: REVIEW 7. Find the resultant geometrically. u V-

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Q: Given the graph of the function f(x) below, use a left Riemann sum with 4 rectangles to approximate…

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

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Q: dy dx 11 1 x log x

A: ∫1xdx=lnx+cdlogxdx=1xdydx=1xlogxdy=1xlogxdxintegrate both side

Q: Find the length of the polar curve r = 8 sin³ (0/3) on 0≤0 ≤π/4.

A: The arc length of a polar curve r=fθ between θ=a and θ=b is given by  ∫abr2+drdθ2dθ Given: r=8sin3θ3…

Q: Find the most general antiderivative for the function Note: Don't enter the +C. It's included for…

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Q: 5. y = 3sin (2x²)

A: Solution: Given data, y=3sin(2x^2)  dy/dx = d/dx [3sin(2x^2)]

Q: Evaluate the integral: sin 2x 39 + cos²x dx

A: Given query is to find the integral.

Q: 1) y = 4cos 30 2) y = 3sin 0 2

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Q: 2. Consider the function g: (-∞, 0) U (0, ∞) → R defined by g(x) A. Find all intervals on which…

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Q: A 25-year old woman burns 300- 20t cal/hr while walking on her treadmill. Her caloric intake from…

A: We need to find total calories burned.

Q: f(x)= |2x - 3| + 8 sin (7x)

A: NOTE: Refresh your page if you can't see any equations. . the given function is

Q: SS (√x + √y) dA, R: 0≤x≤ 1,0 ≤ y ≤1 R

A: The given integral, ∬Rx+ydA, R:0≤x≤1, 0≤y≤1 We have to evaluate this integral. Use the formula…

Q: Write an equation in slope intercept form of the line with the given parametric equation:  X=3T-10…

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Q: x cos 3xdx

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Q: Find the Taylor series generated by fat x = a. f(x) = 4x + 2x² + 3, a = − 3 The Taylor series…

A: We need to find Taylor series.

Q: (b) Let I be an interval and f: IR be increasing. Show that fn(x) = f(x) +, defined on I, is…

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Q: Approximate the area under the curve y = with 4 subdivisions. ³ from x = 0 to x = 2 using a Right…

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Q: - If cos(y) = 3 and y is in the first quadrant, find cot²/ 2

A: Given :- cosy=35, y is in first quadrant

Q: Solve the FIRST ORDER LINEAR D.E. Linear in y y' = x³ - 2xy → when x = 1, y = 1

A: Solve the following

Q: Consider the indefinite integral (25 - 2)5 This can be transformed into a basic integral by lettin…

A: ∫xndx=xn+1n+1+cdxndx=nxn-1

Q: The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every…

A: The above diagram is a general representation of a Ferris wheel. Point 'A' is the starting point and…

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 2 P4(x) =…

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Q: complete the identity below. sin x - cos x / sin x + cos x - sin x / cos x =

A: Given query is to simplify the identity.

Q: Find the first four nonzero terms in the Maclaurin series for cos²x-sinx. (Do not derive the series!…

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Q: 10. Determine whether the following series converge or diverge: (Integral Test) a) En=2 In (n) n 1…

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Q: 3. Using vertical Shrinking and stretching, sketch the graph of the given functions in the same…

A: I have solved step by step in detail....go through the solution

Q: CRED -ments = Syllabus Learning bex ssion 31 Question 1 -2 The graph below shows a rectangular sum…

A: Solve the following

Q: 1. Use the piecewise function below to answer the following and sketch the graph. (3x - 12, -1≤x≤5…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the indefinite integrals of the following. Answer is already given. Show step by step on both…

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Q: Evaluate (Hint: First use the substitution u = √x dx √x and then use integration by parts).

A: let u=xdxndx=nxn-1du=12xdxdx=2xdudx=2udu