The norm defined on the space of 2 points continuous function defined of the closed interval [a,b] is given by ||F||=\sqrt=\int |f(t)|^2 dt, t in [a,b], where \sqrt is the square root IIf||==\sum |f(t)| , for all t in [a,b], where \sqrt is the square root ||f||=\sqrt=\sum |f(ti)|^2, for some ti in O [a,b], i=1,2,3,..., where \sqrt is the square root

Q: Which of the following vertices are adjacent to vertex B? * A B F E AC AEDC AEFC AEDFC

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Q: Prove that a contant ,x ,x^2 are integrable on [a,b

A: Let take a constant c I=∫abcdx=cb-a For x I=∫abxdx=12x2ab=12b2-a2

Q: Suppose ƒ : (a, b) → R is differentiable and that ƒ' : (a,b) → R is bounded. Prove that f: (a, b) →…

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Q: Define f(0, 0) in a way that extends f(x,y)=xy[(x^2-y^2)/(x^2+y^2)] to be continuous at the origin

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Q: Here f: R^2 -> R (x,y) -> 2x^3 +2y^3 -3x^2 +3y^2+6 a) determine critical points f b) determine the…

A: We will find out the required values.

Q: Is the function foo= 1 %3D Integrable over the interval [o,2]? Justify

A: We will show that the given function,                   integrable over the interval.

Q: Express the limit as an integral. lim (8(x)²-3(x) ³)Ax over [0, 3] /=1 X ) dx

A: Express the limit as an integral.limn→∞∑i=1n(8(xi∗)2−3(xi∗)3)Δx over [0, 3]

Q: 4 Find the average value of f(x,y) = (+√y) where 0 ≤ x ≤y and 0 ≤ y ≤ 4.

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Q: Determine whether the series converges. Σ V2k – 1 O The series converges. O The series diverges.

A: Solution: ∑k=1∞12k-13 Definition: If there exists N ≥k so that for all n≥N,f(n)=an is positive,…

Q: Find all continuous positive functions f(if any) defined on [0,1] so that the integral of f(x)dx…

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Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

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Q: Show that the function f defined on [0, 1] by the conditions f=2e when<a<를, -1,2, 3, p=1, 2, 3,...…

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Q: Find all points of continuity of f(x,y) = ( y* (sqrt(x^2+y^2)) / |y| If a) y does not equal to zero…

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Q: Use the Cauchy Picard to solve it : Let D ⊆ R^(2), take initial (t_0,x_0) in D. f : D -&gt; R.…

A: Question: To solve the initial value problem (IVP)  x′=x2+e−t2, x(0) = 0 using the Cauchy-Picard…

Q: Every function which is Riemann 0/3 integrable on [a,b] is continuous. * True O False

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Q: what is the domain of f(x,y,z)=ln(z-y)+xysinz

A: what is the domain of f(x,y,z)=ln(z-y)+xysinz

Q: Exercise: If f:T-R is differentiable at +ETX, prove that (f^)^(t) = (ff... +²^(t) = f^(t) = f*(+)…

A: A proof strategy in mathematics that establishes a proposition for all positive integers is known as…

Q: LaplaceTransform[Piecewise[{{1, 0 ≤ t = 2}}]

A: We will find out the required value.

Q: 1. (Q v P) → (~ P ^ ~Q) F F F F

A: For any propositions P and Q,we have to find out the truth table of given statement.

Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: Consider the function f with the following properties: f is continuous everywhere except at x = 2 •…

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Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: -> Verify Divergence Theorem for the function F x + y? = 9, z = 0 and z 2. = yi + xj + z? k over the…

A: Given :-  Verify Divergence Theorem for the function  F→ = y i^ + x j^ + z2 k^ over the region…

Q: What is the simplified form of F(w,x,y,z)=[(1,3,5,7,12,13,15) Select one: а. F(w,x,y,z)=wz+xz+w'xy…

A: The given function is given by : F(w,x,y,z)=∑1,3,5,7,12,13,15 Let us simplify the function using…

Q: The function fCx) is defined by an integral Vi+8sin't dt %3D Find an expresion for f'(x)

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Q: Consider the function f(x) = kx", where n is an even, positive integer. %3D (a) (3 points) If k < 0,…

A: Consider the equation

Q: All polynomials are Riemann Integrable on any interval [a, b]. All bounded functions on [a, b] are…

A: This is a question from Reimann Integration and Darboux Integration.

Q: Differentiate Using the Fundemental Theorem of Calculus d/dx ∫t * dt   Upper Boundary = Sin(x)…

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Q: Let f(t) = et^2 be an integrable function defined on the closed interval [-x, x] on ℝ. If F is the…

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Q: The function f(x)=4e^x is defined over the interval [-2,3]. Appproximate the area A by partitioning…

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Q: Suppose that ƒ is a Riemann integrable function on [a, b]. Prove, in two lines only, that if f is…

A: Bounded function

Q: Determine the set of points at which the function is continuous. ху if (x, y) + (0, 0) f(x, y) = +…

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Q: Use the limit to find partial derivative of…

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Q: x+y The function f(x,y) is not de_ned at the origin. Is it possible x²+y² define it at the origin…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.