1.5 Approximate f x*dx using Simpson's rule Select one: a. -1.3190104 b. 10.3190104 c. 1.3190104 d. 13.190104

Q: (b) Estimate the R.M.S value of f(x) = sinx - logž + e* starting from 0.2 to 1.4 using (i)…

A: Given: f(x)=sin(x)-logex+ex  Interval from 0.2 to 1.4. The formula for root mean square value is…

Q: Given a decreasing concave up function f(x) on the interval [2, 5] with f(2)=10, f(5)=3, f'(2) =-4,…

A: Given, a decreasing concave up function f(x) on the interval 2, 5 with f(2)=10,  f(5)=3, f'(2)=-4,…

Q: Consider the functionsƒ(x) = sin x and g(x) =4∏2 x(∏ - x).Compute and compare the average values of…

A: Average value of f(x)=sinx on [0,π] is given by: Average value of f(x) is 2/π.

Q: 1.Use Simpson's rule to approximate e*+1 dx sing a regular partition with n-4. Compare the estimate…

A: Given: The function is ∫03 e4x+1 dx

Q: Find the characteristic function for fy(x)=e.

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Q: Given a decreasing concave up function f(x) on the interval [2, 5] with f(2)=10, ƒ(5)=3, f'(2)=-4,…

A: Given, a decreasing concave up function f(x) on the interval [2, 5] with   f(2)=10, f(5)=3, f'(2)=-4…

Q: 2x,0 < x <1 Let f(x) = 10, otherwise (note that X is continuous). a. Calculate E(X): b. Calculate…

A: The question is about to find expected value, variance using given p.d.f Given : f(x)= { 2x…

Q: 3. Consider the function: f (x) = v16 – x² + 2 a. Sketch the graph. b. Using geometric formulas…

A: Given: (a) The above equation can be rewritten as follows, Squaring on both sides, The above…

Q: Compute the average rate of change for g(x) = 4x on the following intervals: %3D A) 0sxs1 B) [-1,1]…

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Q: 1. The values of f(x) over the interval 0Sx<0.5 with dx=0.05 are tabulated as shown f(x) f(x) 10…

A: The given problem is to estimate the value of integral in the given limits of integration using…

Q: Find linearization L(x) of f(x) = tanh=' at a= 0 and use it to estimate f(0.01).

A: Topic:- linearisation

Q: Evaluate y dx using weddle's rule from the following table.

A:

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx (2-x), 0<x <3 f(x) = 0,…

A: Given : The pdf of random variable x is : f(x)=Kx2(2-x),0,x&lt;30,elsewhere We want to find value of…

Q: Let f(x) be defined by f(x) = x − 2 ln(x), for x > 0 Part a: On what intervals (if any) is this…

A: For increasing f'(x)&gt;0

Q: Consider an F-curve with df = (6, 8). Determine the F-value that has area a. 0.01 to its left. b.…

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Q: 3. Find the average value of the following function on the given intervals. (a) f(x)=cosx on [0,…

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Q: 2. (Calculator Permitted) What is the average value of f(x)= cosx on the interval [1,5]? (D) 0.412…

A: As per our guidelines we are suppose to solve first question if the multiple questions are posted.…

Q: Q2/ Find the dirivative for the follwing function y = cosh(x)/ln(x)

A: Given: To Find:

Q: The graph of y = x                                ∫  f(t)dt                               0…

A: The given function is, y=∫0xftdt According to the graph, a). Function f is positive on 1,2∪5,6.…

Q: 5: Let f(x) := H(x) cos x, with 1, x> 0 0, x< 0. H(x) := Define the distribution T, by (Tf, ø) := L…

A: given fx=Hxcosxwhere Hx=1,   x&gt;00,   x&lt;0 also distribution Tf define by Tfϕ=∫ℝfxϕxdx for any…

Q: Q2: Obtain an estimate of tan(0.75) using linear interpolation. 0.3 0.5 0.7 0.9 y 0.3093 0.5463…

A: LINEAR INTERPOLATION The simplest form of interpolation is probably the straight line, connecting…

Q: Let f(x) = Using the centered 3-point formula for 1st derivatives: %3D (x-2): f'(0) & 0.251255 using…

A: Solution:

Q: Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at oC for all t>…

A: The objective is to find an expression for temperature u(x,t) if the initial temperature…

Q: 1 Express the following functions in the form utiv • f(Z) = ln (1+z)

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

Q: Let y = f(x) be an positive increasing function defined for x > 0. The length of the curve described…

A: Given:         Length of curve y=f(x) is between x=0 and x=t is equal to14t4+t2+lnt+4+t2−ln2.

Q: From the Newton's Interpolating function, estimate the function at x₁ = 3m using Forward, Backward,…

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Q: | 4. If f(x) = cos(3x) – In(x + 2), then at what value(s) of x on 0 < x < 3 will the slope of the…

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Q: The error involved in making a certain measurement is a continuous rv X with the following pdf. f(x)…

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Q: Consider function cosh(x – 1) | f (x) = for x E [1,3]. (a) Prove that f is a unimodal function in…

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Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is T6 (the Trapezoid…

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Q: 1 Let f(x) = a) Find the tangent line to the graph of the function at a = 1. %3D y 3D b) Find the…

A: Given - f(x)=1xWe need to find tangent line and normal line to graph of function at x=1 Slope of…

Q: • Let f (x) = cos(x). Use central-difference formula of order 0(h²) with step size h 0.1 , 0.01 ,…

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Q: What is the average value of the function cos² x on [0, x]? Select one: -1/2 undefined None of the…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. Let S(h) denote the composite Simpson's rule approximation of f(x) dx with step 1, f(0.25) = 5,…

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Q: For the following function f(x): -2.15 1 27 dx a) Use Simpson's 3/8 rule to find the area under f(x)…

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Q: 10- f(x) dx using Compute the following estimate of 8- y=f(x) the graph in the figure. 6- S(4) 4- 2-…

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Q: A graph of f(x) is shown above. Estimate the following integral. 3 f(x)dx

A: The figure given in the problem represents the graph of the function fx. From the figure, The…

Q: Use Romberg Infegration to evaluate | f(x)dx with 4-digit accuracy. Start with ho = 1. 0.25 0.50…

A: The given table values: x 0 0.25 0.50 0.75 1 f(x) 1.0000 1.0262 1.0859 1.1540 1.2093 The…

Q: in cubic spline interpelation O Only the st derivative of the splne is continuous at thhe interior…

A: Cubic spline interpolation gives an interpolating polynomial that is smoother and has smaller error…

Q: Consider y=xsin(pi)x over [0,2] Verify the mean value that applies and find all values c satisfying…

A: Find values of c satiating the Mean Value Theorem

Q: 3. Use Simpson's rule to estimate f(x)dx from the following data -2.5 0.5 1.0 1.5 2.0 2.5 f(x)…

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Q: The table below shows the average rates of change for points near In (2) for the function f(x) = e +…

A: We have to find the instantaneous rate of change

Q: Determine the Average Function Value in the given interval of the following: Untitled Question f (x)…

A: The average value of a function f(x) over the interval a,b is given as 1b-a∫abf(x)dx

Q: a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy   limit 0 to ∞ b) Find ∫f(x) dx limit: 1…

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Q: 21] For the following continuous pdf, find: (a) F(X), (b) P(X> 1000), (c) E(X). (d) Var(X). -*/2000…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Q4: integrate the following function f(x,y) for x from z to 2n and for y from 0 to n f(x, y) =…

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Q: Suppose the following data points are generated by a smooth function f(x): 1/3 0.8105 Find the best…

A: Answer

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.