Let (x) be the sum of the natural logarithms of all the primes not exceeding x. Prove that (x) ≤ (x) logx, where 7(x) is the prime counting function and log x is the natural logarithm of x.

Q: Prove that lim n→∞ n -* [₁² ( ₁ + ² ) " e e dx = 1. Justify your answer. n

A: Formula :   limx→∞ 1+axx  =  ea                      Given integral is  limn→∞ ∫121+xnn e-x dx…

Q: €₁ = Let y = 5 -5 and u = 1 . Write y as the sum of two orthogonal vectors, ã₁ in Span {u} and ₂…

A: Given that the vectors  y→=5-5-1  and  u→=1-61   .

Q: Find a formula for an for the recursively defined sequence n+1 a₁ = 1 and an+1 2 an

A: Given that a recursive sequence defined as an+1=n+12an and a1=1   we need to derive a general…

Q: 7. Let C be a curve in space x+y²-2² x+y=2z The equation of the projection of C onto the zz-plane is…

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Q: 1 ··· 7. Compute the orthogonal projection of origin. onto the line through A- 2 and the

A: Let us denote the vector 17 by u. The line through the vector -42 and the origin is spanned by the…

Q: 7. Write the second-order ODE 2y" - 4y' +6y= cos(t), as a linear system (with forcing) for y(t) =…

A: This is about second order differential equation

Q: Use Stokes' theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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Q: The geometry is defined by the blue surface. x₁-2 cm, x2=6 cm, x3 10cm and y₁=6 cm. y₁ ус с x 202 1)…

A: As per the Bartleby Policy, we can answer for only the first question. Please repost the whole…

Q: A motorist starts braking for a stop sign. After t seconds, the distance, in metres, from the front…

A: The given equation is s(t)=62-16t+t2. The distance between the front of the car and the stop sign…

Q: 2. Let T: F→ F3 be the operator given by 4 3 3 T(v) = 4 3 1 4 1 3 Determine μT(x) and find a maximal…

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Q: If g (0, ∞) → (0, ∞) is continuous with limx→0 g(x) = +∞o and Σ an is converging series with…

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Q: Evaluate the triple integral. III. (x - y) dV, where E is enclosed by the surfaces z = x² − 1, z = 1…

A: To solve The triple integral we need to find the limits on integration for x, y and z then we…

Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 1 I = (-1)"x" 75 Find the interval,…

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Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D: P3 → P2…

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Q: rien of the following cntttion fecios represeneste lect the correct answer below 41 ** 4 10 S k * S…

A: Given a differential equation  y'=z+y. We need to draw its direction field. To find direction field…

Q: 3. The following pairs of values of x and y are thought to satisfy the law b Draw a suitable graph…

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Q: 6. Let {u₁, µ2} be an orthogonal basis for R². Express à as a linear combination of the u's. U₁ = 2…

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Q: T₁: Texas State University, 202 c. Let b = 21 X2 2x1 [C] ---- T₂: 12 a. Write matrices A and B such…

A: The given linear transformation are T1x1x2=2x1-x24x1 and T2x1x2x3=x1+bx2-3x33x1+x2+x3. Here b=2.…

Q: Determine the amplitude, midline and period, then find the formula of the function

A: We have to determine the amplitude, midline and period then find the formula of the function.

Q: Prove the given identity using Mathematical Induction n k=1 (k − 1) · k = 0 · 1+1·2+2·3+3.4+. + (n −…

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Q: 5. Use an interval of 0.001 to determine the instantaneous rate of change of the function g(z) = 3z³…

A: To find the instantaneous rate of change of the function g(z) at z = -3, we need to use the…

Q: Compute r πT ( eπTZ) ㅠ

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Q: 6. A rod is rotating in a place the following table gives the angle (radians) through with the rod…

A: Difference table for given data, x = t y = θ ∆y ∆2y ∆3y ∆4y 0 0             0.12       0.2…

Q: 3.2(2) Instructions: Please show your steps/calculations and understanding steps by steps. With the…

A: (A) We are given              f(x) = -2/(x - 3)      Differentiating w.r.t x, we get          f'(x)…

Q: 2. Solve the System of First Order Simultaneous Differential Equations x₁ (1) = x₂(1) ; x₁(0)=0, x₂…

A: The system of differential equations is: x1'(t) = x2(t) x2'(t) = -6x1(t) - 7x2(t) - 3 We can write…

Q: Find the first three nonzero terms, or as many as exist, in the series expansion about x=0 for a…

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Q: Use variation of parameters to solve the given nonhomogeneous system. (-₁ + ) x + (cot (1) 10 X(t):…

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Q: Bonnie runs 1(2)/(3) times as far as John each day. If Bonnie runs 5 miles on Monday, 3(1)/(2) miles…

A: We have to find miles run by John using given data.

Q: Constants: a = 2, b = 2. Consider the linear transformation V : R2 → R2 that reflects over the…

A: 1

Q: Derive 1 + 2 ∞ Σ(3) Η cos(n(φ – θ)) = a? – 2 a? – 2ar cos(θ – φ) + r2

A: Euler's identities:  eit = cos(t)+i sin(t)  e-it = cos(t)-i sin(t) . implies cos(t)=(eit+e-it)/2 .…

Q: 21. 36y(4) 22. y(4) 23. y'" 24. y" 37y" + 4y' + 5y = 0. 0. 8y" + 16y 2y' + 5y y' + y 25. y(4) + 5y"…

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Q: Use technology to produce graphs of f that reveal all the important aspects of the curve. Then use…

A: The critical points occur at f'(x)=0 . The inflection points occur at f''(x)=0.   A function f is…

Q: 2. Find f'(1.1), f"(1.1) from the following table 1.1 1.2 1.3 2.0091 2.0333 2.0692 X f(x) 1.4 2.1143…

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Q: 3. Given matris M below, show that [sin² A Msin B sin C det Msin(A-I) sin(B-C) sin(CA) sin A cos A…

A: Given that the matrix M=sin2Asin A cos Acos2Asin2Bsin B cos Bcos2Bsin2Csin C cos Ccos2C

Q: elect the correct an (2-1)(1+y)(z-3) ***

A: The given differential equation is dydx=2y-11+yx-3. To Check: Which of the given options is correct…

Q: 3. Solve the recurrence relation. an = 2an-1, n ≥ 1; ao = 3

A: A recurrence relation. Kindly Note: As per the company rule, we are supposed to solve one problem…

Q: 1. Electromagnetic waves have a fixed relation between the electric and magnetic fields E, B, and…

A: Use right hand thumb rule ( turn right hand from electric field to magnetic field, thumb gives you…

Q: Consider the following differential equation: y′ =xe^3x −2y, y(0)=0 0≤x≤1, 0≤y≤3.5 show that the…

A: The given differential equation is: y'=xe3x−2y,y(0)=0,0≤x≤1,0≤y≤3.5

Q: Question 5 Use the appropriate test to determine convergence or divergence of the following series.…

A: We can represent a series by the expression ∑n=1∞ an, where an is the nth term and an is a function…

Q: Question 3 Suppose {s} is a sequence which is not bounded above. Construct a monotone subsequence…

A: Given that sn is a sequence which is not bounded above. To construct a monotone sub-sequence snk…

Q: 21. Maple tree diameters in a forest area are normally distributed with a mean of 10 inches and a…

A: Please refer to the solution in next step.

Q: unction Find the similar

A: A real-valued function is given.

Q: 2. Prove that if n is pseudo prime in base a > 1 then n is pesudoprime in infinitely many basis.

A: A pseudoprime is a composite number that passes a certain primality test, even though it is not…

Q: (1) (2) (3) {A→~D, B→~F, ~D → (FV ~E)}__ (A & B) → ~E 1 2 3 4 1 1 2 3 1 {PV Q, Q→R}| ~P→ R A → D…

A: 1. A → ~D 2. B → ~F   ≡   ~B ∨ ~F 3. ~D → F ∨ ~E 4.  Hypothetical Syllogism between 1 and 3…

Q: 9. Matrix A and its reduced echelon form are given. Find the basis of the column space and the basis…

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Q: 23. Given X={80,320, a, a, a, a} an and that x = 100. Determine the value of a.

A: Here, the given X=80,320,a,a,a,a and  x=100 . To Find: The value of a.

Q: how that an = 2n+1 is a solution to the recurrence relation an = 2an-1-1 with a₁ =3.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Use the table to express the following Babylonian numeral as a Hindu-Arabic numeral. V VVV <<<<…

A: We have to express given Babylonian numeral as a Hindu-Arabic numeral.

Q: ven ? is a positive integer, prove that ? is even if and only if 5? + 6 is even. You must use…

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Q: 16. Complete the following statements using discrete, continuous, random, interval. a) A b) A…

A: Two statements where we need to substitute the type of variable in order to complete them.