(a) sigma notation. You may use the following fact: Find the Taylor series of In(x) about a for a > 0. Your answer should be in dk (In x) = (-1)k-1(k – 1)! (k > 1) dak xk (b) Your work should clearly justify your answer. Find the interval of convergence of the Taylor series of In(x) about x = a.

Q: Problem 4. Write a function that has a horizontal asymptote at y=2 and vertical asymptotes at z-1 an...

A: For a rational function fx=gxhx vertical asymptotes are given by hx=0 Horizontal asymptote of a func...

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, xz ...

A:

Q: A box contains 8 red, 5 white, 6 blue and 11 black marbles. If one marble is taken from the box, fin...

A: we have 8 red , 5 white , 6 blue and 11 black marbles if one marble is taken from the box, find the ...

Q: Show that the column space of the matrix A is {(x,y.z) E R³:x+y+z=| 1 -1 0 where A =O 1 -1 00

A:

Q: (Q4) Prove that if f : R → R is continuous function, and (n¡)ieN is a sequence of non-zero natural n...

A:

Q: Hw.4 consider a ctosed Kectangutar box uith a If base side ir measured with evror at 2% and the heig...

A: Volume of the box with square base is given by V=x2ywherex=base sidey=height Surface area of the box...

Q: sinh(3r) Solve for fe(r) given that f(r): %3D 3

A: According to the definition of hyperbolic functions sinhx=e-x-ex2 and coshx=e-x+ex2. The derivative ...

Q: - Find in terms of Jo and J:

A:

Q: if an investment of P750,000 that matures in 15 years but with certain specification that P 500000 w...

A:

Q: (1). Prove that adding an irrational number with a rational number is an irrational number, and show...

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as th...

Q: Prove that F (3x)(A → B) → ()A → (3x)B.

A: We have to prove, ∃xA→B→∀xA→∃xB

Q: How many shortest lattice paths start at (2, 2) and a. end at (10, 10)? b. end at (10, 10) and pass ...

A: Note: As per our guidelines, we are supposed to answer only 3subparts and rest can be reposted.   Fo...

Q: (2) Consider the following LPP where a, b e R: maximize AT1 + br2 subject to 3r2 = 6 T1, 12 >0

A: Since you have asked multiple question, we will solve any one question for you. If you want any spec...

Q: Compute numerically the first real positive root of the following function using bisection method. (...

A: Given,  The function is given by,  X + e-2X-1 = 0 The bisection method is used to find a roots of th...

Q: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1. (-1)...

A: Maclaurain series

Q: Problem: You have a business job where you are helping track revenue and sales. Suppose that p is th...

A:

Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

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

Q: . Find the analytic function, whose real part is sin 2x/(cosh 2y- cos 2x).

A:

Q: 11.7 in. 11.7 in. 10 in. 10.6 in. 10.6 in. 10 in. 10 in. 7 in. 12 in. 10.6 in. 10.6 in. 10 in. 11.7 ...

A: The area of a rectangle is calculated using the formula: A=l×w, where l, w are the length and width ...

Q: Let n e Z. Prove that n² + 4 is divisible by 8 if and only if 3n + 6 is divisible by 12. (Hint: the ...

A:

Q: Problem (2): Show that there are exactly two automorphisms of Q[V2].

A:

Q: root of er one ite

A:

Q: 93.> (@) Find the complute aud singulak integeal 9 the partial alifferential equation + 3p 2 2 3 px

A: Solution a: Given PDE is z=px+qy+3p2q3 Since give PDE is of the type z=px+qy+f(p,q) which is the Cla...

Q: 3. Solve for fel(r) given that f(x)%3= sinh(3r)

A:

Q: Find the area of the region bounded by y=4x^2, y=0 and x=4. Solve in two ways.

A: Let us consider the curve H(x)=f(x)-g(x) then area between the interval [a,b] is obtained as I=∫abH(...

Q: (a) Determine the appropriate Green's function by using the method of variation of parameters for th...

A: Green's Function: The Green’s function approach is particularly better to solve boundary-value probl...

Q: For the function f(x) = v1 +x, let xo = (a) Find the Lagrange interpolating polynomial for f(x). (b)...

A:

Q: Dirt is sold by the cubic yard. The Vining family needs to purchase enough dirt to fill a hole that ...

A: Let us consider a cuboid of length L, breadth B , height H then the volume of the cuboid is Volume o...

Q: 1 Let f (z) z - 8 Part (a) Integrate the function f (z)along the curve C the complex plane given by ...

A: Using the Cauchy integral theorem on the closed contour for part(b).

Q: Solve the following equation, working over Z20 and over Z respectively: a2 + 5y? 322.

A:

Q: (4) Consider the following set: S = {(x, y, z) E R³ | xy + yz + x =-2}. (a) Show that S is a surface...

A: Given: S=x, y, z∈ℝ3| xy+yz+x=-2 To show: a) S is surface. b) Give parametrization of S such that -1,...

Q: QUESTION 1 Determine if the series absolutely converges, conditionally or diverges. Then choose each...

A:

Q: 2. Find the equation of the normal line to the graph of e tan(ry) – In(2? – 3y) = sin (7z) %3D at th...

A: Given curve is  eytanxy-lnx2-3y=sin2πx

Q: Find the positive root of [x e* = 2 ] by the method of false position (show only 5 iterations).

A:

Q: 2. Find in terms of Jo and J,: x²½(x)dx

A:

Q: d. Find D, a diagonal matrix A is similar to. Find C such that CAC = D. e.

A:

Q: Q2). Study each of the following in terms of being finite - countable - finite - then find the max, ...

A:

Q: The alpha level .001 has a corresponding z score of t.002 O True O False

A: Data Given in Question:Alpha level = α = 0.001 Corresponding Z score of ± 0.002  

Q: 9Suppose that the tringle inequality is strict llel veetor s,that means non para V QeR we get on I1 ...

A:

Q: Sletě the following sentences appropriately for a 3 x 3 matrix. If the column space is a plane, the ...

A:

Q: Let P (A) = 0.4 and P (A ∪ B) = 0.6. For what value of P (B) are A and B independent?

A:

Q: Let z, y, z be digits so that the 9-digit number 5z36y98z2 is divisible by 792. a Without calculatin...

A: Given 9 digit number 5x36y98z2 is divisible by 792. (a) Without calculating x,y explain what is the ...

Q: Problem 7. Let Q(3, 1, -6) and let I be the line passing through the point Q and perpen- dicular to ...

A: We have to find the equation of line L.

Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of ...

A:

Q: Can I please get the answer for these?

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for...

Q: Using Theorem 3, find f(t) if L(F) equals: s + 10 ? – s – 2

A: We have , Lf(t) = s + 10s2 - s - 2 We need to find Inverse Laplace Transform , i.e. f(t), Here , F(s...

Q: Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x...

A: Let a ∈ ℝn be fixed.  Given that the vectors x , y ∈ ℝn are related by the equation a = x + x·yy. We...

Q: Question 3 Use Laplace transform technique to solve the initial value problem y + 4y = g(t), y(0) = ...

A: First write the unit step function for the given piecewise function gt.

Q: In a batch of 500 high school students, there are 252 students who own a laptop, 176 students who ow...

A: Here we can use the formula nU = nA+nB-nA∩B+nA∪B' 

Q: Σ. (-1)* 2n+3 R=1 Show you work separately and submit it u absolutely converges

A: Given ∑n=1∞-1π2n+3 taking constant out  ∑n=1∞-1π2n+3=-1π∑n=1∞12n+3