Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated lis If an answer does not exist, enter DNE.) f(x)=√x, [0, 25] C = 0,25 X

Q: dx 5. ≈ 16 x J dx – x2

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: =

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Q: Find the order and degree of e^y" - 3(y¹)² + 2xy = xe² and write the differential equation in noxmal…

A: Follow the procedure given below.

Q: EX: Expand fit) = +² o<t<2π in a Fourier Series expansion : Sel: 2L = 2πT 4 44 L=# -41 2tr 4T 2TT 21…

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Q: = 1. Verify that y(x) = - +12e¹** is a solution of the ordinary differential equation y' = 14y + 1.…

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Q: 20. e ³.x (e²x + 1)² dx

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Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: 2) 2 s² (s²+4) Find L1 transformation. by using the properties of inverse Laplace

A: Given; L-12s2s2+4   As we know from the property of the inverse Laplace transformation.…

Q: 2. (9x-4y+4)dx=(2x−y+1)dy=0

A: Given

Q: Find the center and radius of the circle whose diameter has an endpoint at (3, -4) and the origin. 5…

A: Given that the endpoints of the diameter are 3,-4 and 0,0.

Q: 5. The footbball player played with a ball having a circumference between 30 and 33 inches and a…

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Q: Q/Find the Taylor Polynomials of orders 0,192 and 3 generated by fat a F(x) = Sinx 29=0

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Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)3 ℒ{f(t)} =

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Q: dx (4+x²)² √

A: Explained below

Q: fx arccos x dx 2.

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Q: @ y = x tan 2x

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Q: O =^P^-^2) TAPE 2

A: Topic:- differential equations

Q: 4. 2ydx + (x x³y³) dy = 0

A: Here we have to solve the given differential equation

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2…

A: Since you have posted multiple questions i can do first question in image as per our company…

Q: 1. (4D-23D³-33D²-17D- 2. 2. d^x dx +39³ x db db³ db² -27d²x 62

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Q: Matrixes: find k by determinant K-3 0 1 A = 1 K-3 0 0 1 K-3

A: We have to find K by determinant.

Q: L-1 4s - 10 2 S s² + 25

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Q: dx ex+e-x 2. S dx

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Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

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Q: 15. Find the inverse of matrix A. A = 38 26

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Q: 2. Find the Domain of the function: h (x) = 4x x (x² – 9)

A: Given function h(x)=4xx(x2-9)

Q: Q3: The equation of the tangent line to the graph of y=f(x) at x=-3, f(-3)=2 & f'(-3)=5 is a)…

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Q: The ellipse 3 4 8 16 x²y² 1 = + 9 16 4 has a vertical axis of

A: elipse equation is given  x2/9 + y2/16 = 1/4 here compare with  x2/a2 + y2/b2 = 1

Q: L 1 1 {}} 2 S S + 1 S-6

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Q: Determine the area of the shaded region. 14r y=7x-x² 12 10 8 6 2 y=x (6,6)

A: Solve by integration

Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 71/6 81/5 91/4 62/3 None of…

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Q: Evaluate the integrals. x√√1-x² dx a. x X b. I si sin5 -cos-dx 3 3

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Q: Calculate the are bounded by the curves: C. y = e2x and x - 2y + 5 = 0

A: Area

Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

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Q: Q5: If y=tant and x = cost then at t= is (not that these functions in N) dx a) -1 b) 0 c) d) 1 e)…

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Q: Solve: y(x) dy dx = = (8x² - 7x + 6) (y-7), where y(0) = 11.

A: We will solve the given differetial equation by variable separation method.

Q: What is the indefinite integral of this function?  f (z) = √z (4(z-1)2 + 1/z3)

A: What is the indefinite integral of this function?  f (z) = √z (4(z-1)2 + 1/z3)

Q: Find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = 3t2 − 4 sin(5t) ℒ{f(t)} =

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Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: Express the polar coordinates (2.) as Cartesian coordinates. (√3,1) (-√3,-1) (√3,-1)

A: Topic = Geometry

Q: 5. Using the least squares approximation, the best fit an exponential curve y = = ea(x-b) to the…

A: answer is in next step

Q: Q1: If y=sint and t= sin x, then at x = a) 0 b) c) cosl dx² d) -cosl e) others

A: I have stated the used properties in the solution

Q: 4. (a) (i) Calculate (4 + 6i)².

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Q: If y(z) = √3+ rºdr then 0 y' (2) = 524√√3+25 Q X estion E

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

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Q: See

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Q: Determine the volume generated of the area bounded by y=√√x and y=-x rotated around x=5. 2

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Q: 2 1 x^²({( ²² - ² - ) } L 3 S S

A: Given that,      L-12s-1s32

Q: Given the ordered pair P(-7, 24), determine the requested sine, cosine, or tangent of angle 0. cos 0…

A: On solving this we will get