1. Let H=10 so 100r f (r,b)=[?][?]+1006 . Compute a[2][?]f

Q: 1 is th -1] f'a', for w

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Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Estimate the value of to within 0.057 of its exact value. 3 - n=1 n

A: To find the value of series that comes within an accuracy of 0.057 of its exact value using the…

Q: 2.2 If fe R(a) on [a, b] and if Saf da prove that a must be constant on [a, b]. = 0 for every f…

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Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

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Q: f(z) is analytic in C

A: Given: f(z) is analytic in C.

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

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Q: 5. Recall that we defined In r S4. for r> 0. Prove that In(ry) = In(r) + In(y) for all r, y > 0. (*)…

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Q: 2. f(x) = In 3r on [1,4 with n =5

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Q: If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [O,10]. True False

A: Given

Q: A. Homo ge neous Higher Ordered DE (0-704 - 310° ° + 103o² 1030² + 1500 - 216) y:0

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Q: s(2) f(z) is analytic in C

A: Ans : false

Q: d Prove that (x") = n x"-1 dx

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Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

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Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

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Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: Let a be a constant. Given that 3z° In(ax)dr = e® ( 10 – - -23 find In a. 3

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Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: In(1+2x) Find the Padé approximation R1,2(x) for f(r) %3D

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Q: Let a be a constant. Given that 3x In(ax)dr = e18 ( 36 -89 , find In a. 3

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Q: If f:(0,∞)→Rf:(0,∞)→R is defined by f(x)=xln(2x)f(x)=xln⁡(2x) for every x∈(0,∞),x∈(0,∞),  then…

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Q: Express the following functions in the form u+iv f (2) = In(2)

A: We know that the complex number z=x+iy can be expressed in the form z=r·eiθ where  r = x2+y2 and…

Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

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Q: The function f(x) =x + 1/x is concave upward on none O (-1) O (0,) O (0,1) O (1,)

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Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: Suppose f'(x) = c for all x, where c is a constant. Show that, for some constant d, f(x) = cx + d.

A: suppose f'(x) =c for all x, where c is constant .Show that for some constant d, f(x)=cx+d

Q: 1d. Show that the given equation x- In xX= 0, has a root in the interval [4, 5].

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Q: Find g' (3) . g(x) : In(1+t) dt O In(10) O 6ln(10) O In(4) O 3

A:

Q: Suppose that f e H(C) and |f(2)I < eRez for all z. Show that f(z) ce for some constant c.

A: Consider fz=cez for z=x+i y Take absolute value on both sides: fz=cez=cex+iy=cexeiy=cex…

Q: Calculate dIn |2 – 1|/d In a as a function of 2 and w; by differentiating 2(a) – 1 = H²a? to show d…

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Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

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Q: Compute the following: ( a) Σ, (-1)f (-1)*i i=1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (c) Use part (b) to show that Fn-1 00 00 (-1)"+1 - Fn Fn+1 n=1 Fn+1 n=1

A: Consider the given information: The part (b) states that  -1n+1=Fn2-Fn+1Fn-1 To show that,…

Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: 2. Suppose that f is a measurable function satisfying m({r €R: [f(x)| 2n}) < ne N. n3' Is f…

A: Given that f is a measurable function, with the following condition satisfied. m(x∈ℝ:…

Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: 29 7 dispnove "7z: x?ex" means Provide an a st. x Pow Kat fr がそ.x メ **メ Prove that fn t : x<x!

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Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: 8. If l is the output for Carmichael's function machine shown at right, how can you determine what…

A: Since the output for Carmichael's function machine is 1. Equate x2+2x+1 to the output value of 1 and…

Q: If f is differentiable and non-negative on an interval I in R then /3f + 1 is differentiable on I.

A: The given statement is true. Because when f will be non negative then the derivative of the given…

Q: exists depends on as long as tť? <

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Q: • In z Find F" (2) if F(x) et dt a² _4 O A. 1 O B. 0 Ос. -2 O D. -4 O E. –3

A: Given:         Fx=∫x2-4ln xet dt                 =etx2-4ln x                 =eln x-ex2-4…

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: if |f] is in L^1(A), then his in L^1(A)?

A:

Q: We conclude that: for every additional distress input, the brain activity increases by 0.061 units…

A: Answer:----.               Date:----6/10/2021 since slope is change in dependent variable with 1…

Q: 13. a) Show that EX=o (-1)*(")=0, and then verify that ) +C) + C) + - - G) +G) + () +- ... = b)…

A: We will use of binomial theorem to solve it

Q: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

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Q: Suppose X~N(159,19), and Z~N(0,1). Then x = 126, is equivalent to z = ______. (Round your answer to…

A: We have to find z score for given data...

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.