Consider the function f defined on [0, 1] such thatf (0) = f(1) = 1,f(1/5) = f(3/5) 2, and f (2/5) = f(4/5) composite Trapezoidal rule with 5 subintervals is 1.8, then the value of c is = c. Suppose that the approximation of I = f(x)dx by O -0.5 O 2 O 0.5 O 4

Q: Find the Green's function G" + k²G = 8(x − s), Gʻ(0, s) = 0, G′(0,π) = 0 -

A: To find the Green's function G(x,s) for the given differential equation G′′+k2G=δ(x−s), subject to…

Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: R defined by f(x, y) = 2x³-12x² - 6xy+3y² +24y. Consider the function f: R²- a) Find the Cartesian…

A: If a real function of two variables  is differentiable whose second partial derivatives exists and…

Q: Let f(x) = r e-t dt – 1/2. Find root to f(r) by using bisection method. You should find the interval…

A: As the given integral is improper and have no closed form solution; we will use numerical…

Q: 5. Express the given function using unit step function: * [t f (t) = 0st<4 2 , t24 O A.) f (t) = t…

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Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: If f is the function given by ƒ(x) = √²* √t² — t dt, then ƒ' (2) = 7 a. 2√12 b. √2 c. √12 d. 2√12 B…

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Q: 5. Let f(x, y) = x+4 cos y. (a) Evaluate f (0, z/3), f.(0, z /3) and f,(0, x/3). (b) Use the results…

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Q: Knowing fli) = 3, f (1) = 27. find d (7) at

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Q: Let Find the values of a and b so that f will be differentiable at x = 5. a = b = i √(x) = {2x²+ A…

A: We have been given a piecewise function.. We have to find the values of a and b so that f is…

Q: a) For the function f(x)=x³ –12x + 5, determine i) intervals where f is increasing or decreasing ii)…

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Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z =…

A: Let us consider the given function f(x,y) and (a,b) is critical point then fx=fy=0. Determine…

Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

A: The given function is, fx=-3-6x We need to find the equation of the tangent line to the function at…

Q: What is T₂(x) centered at a = 3 for a function f(x) such that f(3) = 9, f '(3) = 8, f "(3) = 4, and…

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Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: of lf" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only…

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Q: Let F(s)= [f(x-s)d. Find F(s) for the function f(x)= x", where n is a constant.

A: The power rule for integration is ∫x5dx=x66+C. Here, C is the constant and x is the integration…

Q: Q. Find the Z trans form of the following functions by using MATLAB. 1. f(k) = (-2)^(k+3) - 8…

A: Ztransform converts a discrete-time signal into a complex frequency-domain representation.

Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

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Q: Find all the tangents of the graph Gf of the function f(x)=lnx  from Df = [1,e], which are parallel…

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Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.