find derivatie of all the orders of following tting 5(ax`+bx+C/ functions.

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A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: Use part I of the Fundamental Theorem of Calculus to find the deriyative of 12 १৩) | ( ) = dt f'(x)…

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Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

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Q: Find the absolute max and min of the function F(x)= 2sin(x)-cos2(x) on the interval [-π, π]

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Q: Find a finite difference approximation to f"(x) using the points x — x − 2h, x-h, x,x+h,x+2h and…

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Q: Define a weakly quasi-concave on a Cobb-Douglas Function

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Q: Show that the functions are continuous on their natural domains with examples?

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Q: Theorem

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Q: The triangle inequality is the most common algebraic tool for rigorously proving order…

A: Note:- As you want the answer of 4th statement so i am solving only it.

Q: Which of the following family of functions are not known to be globally continuous (ie, contin- uous…

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Q: Let x be a continuous Click the icon to

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Q: Prove that f(x) =- 2x(sinx+ tanx), is an odd function, where [] denotes %3D X+ 2n -3 the greatest…

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Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

Q: 2. If X is a finite set and fn → f on X, show that fn = f on X. 3. If fn 3 f on X and Y is a…

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Q: Define wronskian of Two Functions?

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Q: *=3 is continuous on: x> 3 R-(0,3} R- {2,3} R- {3} R = (-00, 00)

A: Continuity

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A: Using integration by parts solve the integral:  ∫0∞xne-xdx=∫xne-xdx0∞…

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A: It is given that f has a local minimum value at c. Thus, by the concept of local minimum, fc≤fx when…

Q: Find the number of all onto functions from the set {1, 2, 3, ... , n} to itself.

A: Consider the given set {1, 2, 3,…, n}Since the function is onto. So, all elements of {1, 2, 3,…, n}…

Q: Determine all the critical numbers of f(x) = sinxcosx.

A: Determine all the critical numbers of   f(x) = sin(x)cos(x)

Q: 2 prove or DISprove every lpochitz function is differen trablé .

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Q: 1 Show that f (x) = is Libschitz function on %3D x +1

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Q: 5. Determine the interval on which f(x) = x+2 is integrable. %3D (-00, 2) [-2, co0) (-00,-2) U (-2,…

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Q: Show that x + is increasing on [1, 0).

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Q: Show that the function f defined on [0, 1] by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

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Q: draw the graph of a function f on [0, 4] with the given property. Jump discontinuity at x = 2 and…

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Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

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Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

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Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

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

Q: 4. Verify Mean Value Theorem for the function f(x) = 2x ° - 6x2 + 2 in the interval %3D [a, b],…

A: given function :

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Q: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

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Q: estimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?

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Q: Give a proof of the Cauchy's Mean Value Theorem by considering the function F(x) = [f(b) – f(a)]g(x)…

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Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: let ļ be continuous decreasing is an even function, Heen e increasing [-b, -a] on

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Q: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

Q: Use theorem 5.2 to prove directly that the function f(x) = x* is integrable [0, 1]. on

A: Using the given Theorem 5.2 we have to prove directly that the function fx=x3 is integrable on [0,…

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…

Q: (4) Are all entire functions bounded on D?

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…

Q: Present a combinatorial argument to justify your answer. How many increasing (not strictly)…

A: We have to find find total number of increasing functions from {1,2,3,...,n} to {0,1}. As a function…