Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0

Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: 2. The table shows values of the function y = G(t). Use the table to estimate the value of 50…

A: Physical significance of integration is calculation of area under the curve. Here discrete values at…

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

Q: Which of the following equations is/are exact? □ 3x²y² dx + (2x³y + 4y³) dy = 0 (3x²y-x²) dx + e³ dy…

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Q: Find the volume of the solid generated when the region bounded by y = 5x and y= 15√√x is revolved…

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Q: Eliminate A and B. y=Ae2x+Bxe2x Oy -4y2y=0 Oy +4y +4y=0 Oy²-2y-4y=0 |y-4y +4y=0

A: Given a solution of differential equation as y=Ae2x+Bxe2x. We need to eliminate constants A and B,…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that,            The solid is obtained by rotating the region bounded by the given curves…

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: 22) A- Find the distance between the line (y=x+3) and center of circle (x²+y²-2x=0). B- Using…

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Q: 1 1+exte -X dx

A: Yo evaluate the integral.

Q: Solve the differential equation: dy = A - By. Find the general solution to the dx differential…

A: We need to find out the general solution and particular solution for the given differential…

Q: 21. If u = - y+z a) 0 Z z+x x+y b) 1 ди then the value of x + y + z 2 is: c) u d) None 22. The…

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Q: Given f''(x) = 2x + 5 and f'(0) = Find f'(x) and find f(3) = 1 and f(0) = = = -1.

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Q: 33. Cost A manufacturer has an order for 1000 units of fine paper that can be produced at two…

A: Given data:- Order value of fine paper = 1000 units Produced at two location, x1 & x2 The cost…

Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Evaluate the integral. -^x dx e S² sin √1-x² 2

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Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

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Q: n=1 n²2n-1 (-5)n

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Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: For the function f(x)=ln(1−5x)​, find the Taylor polynomials of orders​ 0, 1,​ 2, and 3 generated by…

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Q: Find the sum of the following: 1 Σ 5n² +5n n=1 a. b. n=1 3+2-1 4n

A: a) ∑n=1∞15n2+5nb) ∑n=1∞3+2n-14n series converges: The series  ∑n=1∞an converges to k, then the…

Q: Find the standard form of the equation of each ellipse. 9. 10. hori 16. 5 on test ор and ← 25 Find…

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Q: 3. I Find all eigenvalues and eigenvectors of: [100] 4-6 A = 0 0 2 0 2 0

A: We have to find eigen values and vector

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: area is given by the function x^0.5+y^0.5=1

A: We have to find the area of given function.

Q: to find all the second order partial derivatives of the given function. The function is f(x, y) =…

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Q: Use integration to find the area of the rose curve r = cos 20.

A: Area bounded by the polar curve Area=12∫ab r2 dθ

Q: S-ydx + xd - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O O 2

A: Solution is given below:

Q: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1) and the following boundary…

A: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1)

Q: Find the derivative of the function. q= 5 3 x + 6x

A: The given function q=x3+6x5

Q: Find the right match for the following ODEs in the dropdown menu y' = y" JS sin(x) 5xy' = y - 3x²y"…

A: This is a problem related to differential equation. Please find the answer as below.

Q: ล. b. TM8 M8 n=1 n=1 (−1)n-1(x - 1)n n2n n! (x − 3)” 272

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Q: [sin¹ 3x cos² 3xdx

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Q: '() = xp (x-₂x) + xp (x + xx7)

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Q: 8] n=1 1 n√n +1

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Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: At what time between 4 and 5 o'clock will the hands of the clock be opposite each other?

A: We have to solve given Questions.

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Find da d.t da dt at x = 4 if y = 4x² – 1 and > Next Question dy dt = - 5.

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Q: Consider the following function and point. x + 4 (5,9) X-4 (a) Find the derivative of the function.…

A: The given function is fx=x+4x-4, 5,9

Q: Find the slope of the tangent line to the curve - x² – 3xy + 3y³ = at the point (1, − 3). - 91

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Q: the degree of the following polynomials functions: a. f(x) = x^5  b. f(x) = (x^2)^3  c. A cubic…

A: Given the query is to find the degree of the polynomial.

Q: -2 1. Ella thinks that if a function is positive over an interval, then its derivative is also…

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Q: PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y =…

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Q: If 6√√x + 15√y = 177, find y'(x) by implicit differentiation. y'(x) = Y I Find the exact value for…

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Q: Q 14) Does the sequence converge or diverge. If it​ converges, find the limit.

A: Concept: Infinite series converges and diverges: Let ∑k=1∞ak be an infinite series, and let an be…

Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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