Q2. Give a counterexample about a bounded function that is not Riemann integrable.

Q: is uniformly continuous by definition on the interval (-1,1) . 4 - * Show that f(x) =

A: A function fx defined on an open intervala,b is uniformly continuous on a,b iff  i fx is continuous…

Q: Find a first degree approximation of f (x) = In x centered at x = 1.

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

Q: Find the formula for the function represented by the integral dt 6t+3 %3D

A: use the substitution method  for finding the integral

Q: Iff: [a,b] R is bounded and has only a finit number of discontinuous points, then f is Riemann…

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Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: State the Comparison Theorem for Improper Integrals. As well, use it to determine whether I+2 dr…

A: The comparison test states that if limx→∞f(x)g(x) is finite and non-zero, then ∫f(x)dx and ∫g(x)dx…

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: What is the definition of f(x) is continuous at x = a? ||

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Q: Is the function F (x) = L", e“ dt concave (concave down) or convex (concave up) for x<0?

A: To solve the following problem

Q: Clarify that f f :(0,1) →R defined by f(x): not uniformly continuous. =-

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: x² +3 dx 2 2x* +x 00 4 1

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Q: Evaluate f x2 dx using the limit defintion of the definite integral.

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Q: Verify Cauchy's MVT for f(x) and f'(x) in [4,9] where f(x) = Vx %3D

A: Cauchy's MVT : If two functions f(x) and g(x) are continues on [a, b] and differentiable on (a, b),…

Q: Express the limit as a definite integral.

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Q: If f (s Continuous then on -fex) True or felse?

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Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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

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Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

Q: Locate and classify the local extremum of f when f(x, y) 4.x2 – 6x – 6y² – 4y + 10xy. - - 1 1.…

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Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x".] lim 5 i = 1 1 dx

A: To express the limit as a definite integral, limn→∞∑i=1n3i4n5

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: Determine the set of points at which the function F(x, y) = arctan ( 3x +7/y – 7 ) is continuous.

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Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

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Q: Use the Cauchy-Riemann equations to show that the function f(z) - e² is not analytic anywhere.

A: The solution is given as

Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Where is f(a) not continuous?

A: Given:

Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x) F(x) |Vt4 + 1 dt -7

A: 2nd Fundamental Theorem : For F(x)=∫axf(t) dt, if f is continues on [a, x], then F'(x)=f(x).

Q: If ƒ is continuous and f(t) dt = 16, find the integral

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Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

A: Given: g(x)=lnxif x&gt;00if x≤0 To check: Whether the given function is Riemann integrable on 0, 2…

Q: Which of the following is always true for integrable functions f and g?

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Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

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Q: b) Compute the integral of the function using the trapezoidal rule, Simpson's 1/3 rule, and…

A: We'll answer one question, since the exact one wasn't specified. Please re submit the question which…

Q: If f is integrable on [a,b], show by example that F (t) = | f (x) dx is continuous but need not to…

A: We need to show by an example that if f is integrable on [a, b], then F(t) (as defined in the…

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: Determine local extremum f(x,g) = xy(4-x-). %3D

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Q: Every function which is riemann integrable on [a, b] is continuous.true or false

A: To check if every function which is riemann integrable on [a, b] is continuous or not.

Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

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Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

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

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