103. Show that In (1 + e²*) = 2x + In(1 + e-*).

Q: 4. P1,500 payable semi-annually at 6% effective o bn qon

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Q: (22-4) (교3-4z)3 dz

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Q: 2 Evaluate: :S,vte-t² dt.

A: Detailed explanation mentioned below

Q: If In æ + In(x – 7) = ln(7x), then æ

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Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: Show that, cosh-1 x = In (x + /x² – 1)|

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Q: السؤال 2 when hv hvo Electron is ejected from surface of metal ylgn O

A: Since we know that​ The ejected electrons have a distribution from 0 to  hv-hv0

Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫lnx-lnx-...dx To find the given integral in terms of some new variables t

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: 5. Show that Beta(a,b) belongs to the 2-parameter exponential family

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Q: Evaluate the integral: */64 – a°dz .3 2 -

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Q: In x /1+ (In x)² -dp-

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Q: A factory received a shipment of 11 lightbulbs, and the vendor who sold the items knows there are 3…

A: Given in the question: Total bulbs, N = 11 Defective bulbs, x = 3 Now we will calculate the sample…

Q: Find indefinite integral e2x - p- e2x +1

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Q: d) 85% of all students finish the activity in less than secon Submit Question

A: X~N( μ = 38.6 , ? = 6.3 ) μ = 38.6 , ? = 6.3 Z-score =( x - μ )/?

Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: 3 E in (1 -) -in2 , . =-In2 =1 k2 –1 k=2

A: We will  use the limit of partial sum

Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

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Q: 3, Re call Eudlid's proof of In finitude * primes! Shouw that T Cx): = 1{ ps X: p-pinae }12 logz…

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Q: Evaluate the improper integral : [* 4x°e=9¤*•

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Q: Suppose that there are currently unemployed workers în some state. Each mðnth 8% of all those…

A: Given data: Number of unemployed workers=25,000 Let x be the number of months. Given that each month…

Q: Show that - In(x – V - 1) = In(x + Vr – 1)

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Q: (-1)" -Σ S. n=1 Vn+1

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Q: 1.al If 123x 78425167 is a muitiple of 1l, tind x.

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Q: -2x -dx - Evaluate (1-x)' 8 А. х* + 6х- In(1-х)' + 1-х 8 -(1-x)* +C С. х? +6х+ In(1-х)' +- -(1–x)*…

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Q: Suppose that 0< fn < In on X for all n e N. If gn 30 on X, then fn 30 on X.

A: Solution:-

Q: If In x + In(x – 2) = ln(7x), then x -

A: From the given problem:   lnx+lnx-2=ln7x   Now using the logarithmic property:   ln(a·b)=ln(a)+ln(b)

Q: .5. Compute integral -3 (2.p) -5 5.

A: Given: So, we have f(x)=0,   x≤2c,   x&gt;2.

Q: Prove that In (1tx) Lx for without using the value the orem. mean

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Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Let n e Z. n#-1,3,

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Q: 23. -(-Cnd)→e -evd dz

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Q: Using the Simson Scientist Rule4n Psychological Summit Integral O 0.69312 O 0.69317 O 0.69320 O…

A: According to Bartleby guidelines we are supposed to solve a question at a time. Please upload the…

Q: Find the derivative of 4 ^ (3x) * O 12x O In 4 O x In 64 O (4^(3x)) In 64

A: We can solve this question taking derivative of both side wrt x

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: 15. Find the general solution of dr bcosedr + rsinode

A: General solution of differential equation

Q: ν4-x (h) N(x)=; In|x|–1

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Q: Write In (e5 x 2) in term of In x. In (e x²) =

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Q: 16. Integral Ydy 6y2-1

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Q: (15 49)} = at* e²¹ sen(71), et 2-¹ {-98 (8-2)² +49)} = What's the value of a*c?

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Q: Evaluate the integral.

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Q: Show that dx = x² – 8x In (7 + 4/3). -

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Q: Suppose thát the captain of a ship that is in distress must send a

A: sollution is given below:

Q: If In x + In(x - 7) = ln(7x), then x =

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Q: Compute 0. pleafe be Fimft e Fast and Show your wonkings.

A: See the attachment

Q: 1.Find the interval and radius of conv. of In(1 - x2) ?

A: Maclurin series representation for ln(1- x2 ) is  ∑n=0∞-(x)2n +2n+1   (Why?) Explanation As ln(1+x)…

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A: