Give a proof by cases that [4x] = [x] + [x + ¼ ]+ [x + ½ ] + [x + ¾ ] %3D

Q: Use the def'n of to test the dif ferentiability of the x=0 : ヘ人る given gn at Sx²+2x-1, x<o ○け f(x) =…

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Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: Differentiate the following with respect to X: In(x? + 3x +5) X A. x² + 3x +5 В. 2x +3 x2 + 3x +5 3…

A: Let, f(x)=ln(x2+3x+5) is the function. We have to find the derivative of this function with respect…

Q: Find the derivative

A: Given function is  By using the properties of log  log(m)-log(n)=log(m/n) and log (m^n)=nlog(m), we…

Q: f'(2) for (x- x)(x² +2)(x² +x- 1) S(x) = %3D x + 2 O 676/5 O 379/7 O 587/3 O 384/9 O 585/4 O 699/7

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Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

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Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

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Q: A) Evaluate the following integral (x - 1)(x − 2)(x-3) -

A: Given, ∫1x-1x-2x-3dx

Q: On what intervals is f(æ) = x³ +3x² – 24r+7 increasing? The graph is increasing on the intervals OD…

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Q: a. Solve b. Determine whether each of these functions is a bijection from Z to Z. f (n) = n² + 1

A: A function is said to be bijective, if it has both injective and surjective properties. Meaning the…

Q: Use the residue theorem to evaluate: o dx 0 x3+1 2n/3

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Q: Find a general formula for dr ax + b dx" cx +d

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Q: (b) Expand and simplify in ascending powers of x as far as the term in x" 1+3x

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Q: Find the integral. [6+xx4-x2) dx O a 5 +C 20x- b. 20 -x* -c +C 20x O d 20x LEGO

A: Integration problem.....

Q: Q3 : Evaluate the following integral. x+V9-x2 xps

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Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: ts] Transform the following to principal аxes: а. 5xỉ + 2x1x2 + 5x3 = 10

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Q: Q3 : Evaluate the following integral. X4V9-x2

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Q: For any n large enough, prove E" ) – = 0(1). k=0

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Q: Evaluate the following integral. V3 + 5 2 13 dx 12x - 12x+ 28 2 V3 +5 23 dx (Type an exact answer.)…

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Q: 2 ー (4-x²) dx -2

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Q: For f(x) = x³ - x +4, compute the formula for n+1 in Newton's method. - In +4 - 3h - In 3a급-1 | In +…

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Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: 6. (a) Express f (x), where x3 + 1 f(x) = %3D (x – 1)2 (x² + 1) Hence, or, otherwise, find HE AND…

A: f(x)=x3+1(x-1)2(x2+1)

Q: Evaluate f (2x + 1) dx by two methods: (a) Expand (2.x +.1)' by the binomial theorem; (b) let u = 2x…

A: Given that ∫2x+13dxa. using binomial…

Q: (a) Evaluate the integral ∫0 ∞x ne-x dx for n=0, 1,2 and 3.(b) Guess the value of ∫0 ∞x ne-x dx when…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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: Let f(x)=X13, ga)= 2R-1, and h(x) : 2x* + 2n-12. Wiite a formula and Simplify for: (fh)(x)= ell

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Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

A: Given that X is a random variable which has binomial distribution Bn,θ with p.d.f is given by:…

Q: Use the definition in terms of exponential functions to prove the following 1.tanh(In x) %3D x2+1

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Q: Use symmetry to evaluate the followingintegrals.

A: The given equation is ∫-223x8-2dx The symmetric property for integral is expressed as…

Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: Compute the definite integral (x + 4) In(x²)d.x.

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Q: Use symmetry to evaluate the following integral. 7. 2. So- |(3- |x) dx -2

A: The given integral is,

Q: Evaluate the following integral 1 x² +6x+13

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Q: Sove for X: 3+ In(x+2)=2 .do not round any intermediate Computeltions; and round your answer. to the…

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Q: Consider f(x) = 2x +3. Is f : N → N one-to-one? Is it onto? Prove, or give counterexample.

A: As per our guidelines we can answer only one question. please repost other seperately

Q: ½t² Show that M₂(E)=é

A: Xi~Nμ,σ2X~Nμ,σ2nZ=X -μσn~N0,1 X is a linear combination of independent normal random variables…

Q: The characteristic of Zs[x]/ is 6. 3 O None of the choices

A: The characteristics of the function

Q: solve. write your anS w ers in suentific (-3.4 x 10*) + (5.2 x 10*) © (6.812 x 102") + (4. 3 x 102)…

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Q: Q7: Use the MEAN-VALUE-THEOREM to show that x -1<e* < 2x +1, 0<x<In 2.

A: The solution are next step..

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: (a) Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and…

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Q: Determine a constant k such that (kA)" (kA) = 1, where -2 A = Is there more than one value of k that…

A: Given: kATkA=1 A=-21-1

Q: Show that f (r) = x³ – 3x2 + 2 is monotonically increasing on every interval.

A: Given that: f(x)=x3-3x2+2

Q: 1. Evaluate the following. Use only the rules and techniques of integration presented in the module.…

A: To evaluate the given integral.