and has real 2erar. find no necessary and sufficient conditions P(x) dx. 9(x) or convergencer of

Q: In approximating the root of f (x) = -13 - 20x +1922 - 3x3 |3D using the Bisection Method on the…

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Q: ditions of value theo

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Q: Consider the following equation f(x) = a3 – 3x2 + 3x – 1 = 0, [0.5, 1.5] Determine a function g(x)…

A: given fx=x3-3x2+3x-1 with interval 0.5,1.5 a)  put x=0.5 into the equation of function…

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Q: Let f(x) = = x³ - 2x + 1, to solve the root finding problem f(x) = 0, derive each of the following 1…

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Q: 17. Show that f(x) = x² +2x is uniformly continuous on the interval [0, 10], using the e -8…

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Q: If g(x): = sin x, show that the remainder term in Taylor's Theorem converges to zero as n→∞ for each…

A: g(x): = sin x

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Q: f'(x) = (x+) (x-1) (x+ 7)(x-4)

A: We have givenf'(x) =(x+1)(x-1)(x+7)(x-4)A) critical points are at which f'(x) =0so,f'(x)…

Q: 6. Show that there does not exist a sequence of polynomials converging uniformly on R to f if (i)…

A: A sequence is said to be convergent sequence if it eventually reaches a certain real value as the…

Q: In(x) f(x) = хе (1,0) x-1 In (x) O f(x) = х (1,00) (x-1)a'

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Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: (b). Use the definition of the derivative to evaluate f(x)=x". Hint: Use the Binomial Theorem:…

A: b) Given function is f(x)=xn  We have to find the derivative of f(x)=xn by using the definition of…

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Q: Suppose f is continuous on [1, 5] and the only solutions of the equation f(x) = 6 are x = 1 and x =…

A: Given that suppose f is continuous on [1,5] and the only solutions of the equation f(x)=6 are x=1…

Q: 11. TRUE or FALSE. Identify if the statement is true or false. If True, then prove or explain. If it…

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Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

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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.