het f - - f: R > R be f (x) # x 21, x > 1 graph of f that 1₂ is continuous at Whether f is differentiable at 1. - Shetch Prove Prove के the function Sin (x-1)

Q: One of the following statements is true:

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Q: Consider the following subsets of real plane R² A = {(0,y): ≤ y ≤ 1} B = {(x, y): 0 ≤ x ≤ 1, y =…

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Q: Convert f(t) in terms of step functions and find the Laplace transform using appropriate property. S…

A: Solution

Q: 1 : Prove that the function f(x,x)= defined on the domain , is a convex function. For this purpose,…

A: Here we find  determinant of the hessian matrix. Which is positive on its Domain.

Q: F(s) = = S (s+1)5

A: We find the inverse laplace of  F(s)=s/(s+1)5

Q: Find all the local maxima, local minima, and saddle points of the function. f(x, y) =…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 7. An outdoor swimming pool loses 0.05% of its water volume every day it is in use, due to losses…

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Q: out a calculator?

A: To find the tan inverse of 3/2 and larger than 1 as,

Q: 1. Find the general solution. Indicate which method you are using. Show the details of your work. y'…

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Q: Find (a) the Fourier cosine series (b) the Fourier sine series. Please list the answer to at least 3…

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Q: In one area of the Bay of Fundy, the tides cause the water level to rise to 6 m above average sea…

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Q: 5. Given that G(x, y) = (x² + 1, y²) and F(u, v) = (u + v, v²), compute the Jacobian derivative…

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Q: Determine whether the differential equation is exact. If it is exact, find the solution. (8x² − 2xy…

A: Comparing the given differential equation with the general differential equation Mdx+Ndy=0 we get,…

Q: Let a and b be natural numbers and define d = gcd(a, b). Prove that alb iff d = a. For all sets A,…

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Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: 2- By using Chain Rule, find du/dx, du/dy, du/dz at (x, y, z)=(√3,2,1) P-q U= q-r p=x+y+z q=x-y+z,…

A: This is the question of partial derivative.

Q: x^2 + 5x - y = 6; y = 0; x = 3

A: Please see the attachment  According to the guidelines we are supposed to do one problem.

Q: calculator?

A: To find the inverse of 3/2 and larger than 1 as,

Q: Which of the following is the homogeneous differential equation? A. (3x - 5)dx = (4y - 1)dy B. xydx-…

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Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,…

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Q: x sinx find dy for y dx √(x-1) (x²+1) Evaluate f(u² + 2u + 3)² (u + 1)du

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Q: (b) Compute using polar coordinates quadrant common between circle x² + y² = 2x and circle x² + y² =…

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Q: Q2-By using Chain Rule, find au/ax, du/dy, du/dz at (x, y, z) = (√√3,2,1) U= p-q q-r p=x+y+z…

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Q: 17. y' + y³ = 0, y(0) = yo

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Q: : Prove that the function f(x)=Ln x, defined on the domain R₁, is a concave function. For this…

A: Here Hessian matrix going to be 1×1 matrix.

Q: 9. dy 在 2 1+y²

A: Sol

Q: Graph the inequality subject to the nonnegative restrictions. 15x-24y <0, x ≥ 0, y ≥0 Use the…

A: Sol

Q: Solve the following x²-x²-√√2x lime-21 x²-11x+18

A: Use L' Hospital Rule to evaluate the required limit as in next step.

Q: Suppose you are given a weighted graph with vertices labeled from A to Z. While performing the…

A: Here we have to use Dijkstra's Algorithm to solve this question in this algorithm firstly we assign…

Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: The value of the following = (2+ sin 2x³) / = (2+ sin 2x³) Using the trapezoid integration dx…

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solid is symmetric about y axis, so the centroid lies on y axis.

Q: Q5) Minimize f(x) = (10x³ + 3x² + x + 5)²; using swann's method. Start with x,-3 and step size |A| =…

A: We know that Swann's method iteration formula is  xn+1=xn+2nh where h is step size Condition for…

Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

A: Given information 1.   The domain of f(x) is  -∞,  ∞ 2.  f'x = 5x2 x2 -3 3. f''x = 10 x 2x2 -3 4.…

Q: -) Determine the first six terms of the sequence defined by t₁ = -5 and t = 3t-1 + 8. 5, 23, -61,…

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Q: er, explicit ODE

A: Note:-  For this problem, I'll provide you definition and example of first order explicit ode and…

Q: 41. Two straight roads diverge from an intersection at an angle of 60°. Two cars leave the…

A: Cosine formula  In a triangle ABC if a.b.c denotes sides opposite to angles A,B,C respectively i.e.…

Q: (a) Evaluate the surface integral JL. TU xy ds where D is part of the plane x+y+3z = 3 that lies in…

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Q: 4. While visiting Newfoundland, Ray notices that that the water level at a town dock changes during…

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Q: Find the nth root of the matrix B. An nth root of a matrix B is a matrix A such that A = B. 64 0 0 B…

A: The given matrix is                      B=64000-1000343. B is a diagonal matrix matrix. Here we…

Q: 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine…

A: We need to use given data to sketch the graph . Use relation between degree and radian to get angles…

Q: II. Determine whether each of the following statements about Fibonacci numbers is true or false. a.…

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Q: Show that the differential equation x³y² + x(1+yº)y'′ = 0 is not exact, but becomes exact when…

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Q: Consider the following matrix (a) Compute the determinant of the matrix by expanding along the…

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Q: Marisa has just won a contest. She must decide between two prize options. Collect a lump-sum payment…

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Q: 2. Describe the geometry of the linear transformation represented by each matrix. Explain. 3 0 a. ^=…

A: Follow the steps.

Q: Q4\A/ Five fair coins are flipped, find the probability mass function of the number of heads…

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Q: Find the upper Riemann sum U(f, P) and the lower Riemann sum L(f, P) for each of the following…

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Q: 3. The heights of a stand of pine trees were measured along with the area under the cone formed by…

A: Since u already know a,b,c Let me give u brief answers of them so that we clearly understand d e,f…

Q: Prove that sin²x x cos²x x = csc²x-cot²x 4csc²2x

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