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

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Q: Let F(t) = 4t 1+4t² 1-4t² 1+ 4t² j Using Corollary 12.11, show that F(t)*F' (t) = 0 for all t. i+

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Q: f(x) = 2x² + x + 3. a) Show that if you use the newton method on the function f(x) it not converges,…

A: Newton;'s method can be used to calculate the root of the function. The formula for Newton's method…

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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)…

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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: Use the Second Fundamental Theorem of Calculus to find F'(x). • L₁ VE 4 + 4 dt Vt Step 1 F(x) = Note…

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Q: . The average value of f(x)=√(4-x^2) on [-2, 2] is 1/2 True False The function f(x) * f(x) = x² + 1…

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Q: If the function f is continuous on [0,00) and | f(x)dx is convergent, then there is a possibility…

A: If the function fIs continuous on [0, ∞) and ∫1∞f(x)dx is covergent, then there  is a possiblility…

Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

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…

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Q: or (8) in Section 8.6 to find upper bounds for the error in approximating Trapezoidal Rule Simpson's…

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Q: 11. (a) Let F(s) = L{f(t)}, where f(t) is piecewise continuous and of exponential order on [0, ∞o).…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

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Q: 2. Let g: RR be a measurable function such that fx|g|dm <∞ (here m is the Lebesgue measure). Show…

A: The solution is given below:

Q: 3. F(x) = n(1+t)dt Prove that the function f(x) = cor In(1+z) is Riemann integrable on (0,27]

A: To find the derivative of the given function , you can use the Leibniz rule, which states that if ,…

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A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

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.