3 42 2 -1 3 Let B = Compute det(B) by hand by reducing B to upper -1 31 triangular form using row operations and then applying theorems about determinants and row operations from Section DRD of Beezer.

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. log(x+3) 4. lim…

A: Limit of the function

Q: m [tan ¹(log3 x)+7cosh z z]

A:

Q: KeyConcept Law of Cosines In AABC, if sides with lengths a, b, and care opposite angles with…

A: Consider the given triangle △ABC. Here, a=9, b=7 and c=12. We have to find the angle A, B and C.…

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform 0 ≤ t 0) ]de dt

A:

Q: A = 2 3 2 3 -2 -2 -2 -2 11 7|2 7|27|2 -IN 1 1 22 1 1 1 2 1 -IN 2 1 1 45 01

A: Follow the python script.

Q: dx 1+x method. Hence find the value of log 2. Example 8.18. Evaluate f **M ** HILE correct to three…

A: We need to find log 2 using Romberg's method.

Q: Let X be a normed space, Xn, Yn EX such that Xnx, Yny, then 1-Xn + Yn → 4- ||xn-ynll→→llx - yll.…

A: Given that X is a normed space, xn, yn ∈X such that xn→x, yn→y. To find: 1. xn+ yn→x+y…

Q: Integrate the following functions Ver R: f(x,y) = 3x-2y. the given regi the circle x² + y² registre

A:

Q: Exercise 15.2.21. For each of the following multiplication tables, fill in the blanks to make a…

A: To make a group in caley table , every element in that group appear in each  row and each column…

Q: Q2) Which of the following series is converge or diverge 8 Σ{}} ,0.7777777777777 η2 n=1 } Σ n=1 εισ…

A:

Q: a. [=³² (n =)²] 15. lim z→0+

A:

Q: Evaluate fő ·∙log 1+ax dx 1-ax x√√1-x² ). (1+

A:

Q: The amount of water, A, in thousands of litres, available in a water tank located on a farm…

A: Given: The amount of water, A, in thousands of litres, available in a water tank located on a farm…

Q: | Example 8.20. Evaluate the integral to 3 decimal places. 0.5 x dx using Romberg's method, correct…

A: We need to use romberg's method to solve this problem.

Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…

A:

Q: Test the convergence of the power series below: (-2)" Σ - 3η – 2 (3x – 5)" n=1

A: Consider ∑n=1∞-2n3n-23x-5nTo find: Interval of convergence.

Q: Solve the following Initial Value Problem using Laplace transfo -9t y" - 12y + 11y = e ;y (0) = 1,…

A: The given equation is y''-12y'+11y=e-9t Taking Laplace transform on both sides Ly''-12y'+11y=Le-9t…

Q: 1. Let 7 = {1,2). a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) = 0}. b. Draw the the…

A:

Q: y" ~2y² + 5y = 4e²x cos2x

A: Solution of the non- homogeneous higher order differential equations.

Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

A:

Q: log: (x+3) 2-1-1-cosh(cos-¹x) 4. lim

A:

Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A:

Q: Identify whether the statement is a tautology, a contradiction, or neither of the two. → (PV → (p ^…

A:

Q: Example 10.13. Using Euler's modified method, obtain a solution of the equation dyldx = x + √√y, Eth…

A: The given differential equation is: dydx=x+|y|. here f(x,y)=x+|y|       x(0)=1, 0≤x≤0.6, h=0.2. To…

Q: Three years ago, Pete took out a loan of $55,000.  The loan was taken out for 10 years with an…

A:

Q: Let α =21/8 and let K = Q(α,i). Show that (a) K is the splitting field of x8 −2 over Q and dimQ(K) =…

A: Given: α=218 and K=Qα,i.   To show: K is a splitting field of x8-2 over ℚ and dimℚK=16

Q: Find two unit vectors orthogonal to a = (-2,-1, 3) and b = (5,-2, 1) Enter your answer so that the…

A:

Q: Prove that for every integer x, x+4 is odd if and only if x+7 is even

A: An even number is defined as an integer of the form n = 2k, where k is an integer. An odd number is…

Q: [MO22] Express as a single power series form: 00 (3n+2)an-1(x + 2)n+3 - Σ(5n - 2) an(x + 2)n-1 n=-1…

A:

Q: II. Given: ‘sinh r − 1 if x 2 x-2 Determine if f is continuous or discontinuous at x = 0 and at x =…

A: Types of discontinuous of the pice wise continuous function

Q: Identify the fireze pattern type that is formed when an infinite number of the given letter are…

A: As per the question we have to identify the fireze group of the patterns formed when an infinite…

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = e* sin(t), z =…

A: Curvature and radius of converges

Q: A continuous X Co F(x1= ++x o BX C1 K 1 ≤X Find value of k V-V- X has CDF 16 17 18 19 20 21

A: Given CDF is F(X) = 0,x<012x,0≤x<1k,1≤x

Q: My – Ng N If = Q, where Q is a function of x only, then the differential equation M + Ny = 0 has an…

A:

Q: f(x,y) = 3x-2y. R: the circle x² + y²

A:

Q: V. Given: 2. Find f'(2), if it exists. el3r-6-2, f(x)=[2x - 5], √x²-9, if r ≤ 2 if 2 3

A: Given fx=e3x-6-2,if x≤22x-5,if 2<x≤3x2-9,if x>3

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: # A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than…

Q: Let f(x) be an irreducible cubic over Q with cyclic Galois group. Show that all roots of f(x) are…

A:

Q: H-w.4 Find the volumes for the following solids whose heights are defined by ZCx,y) and bases are…

A: To find volume for the solid whose height is defined by z(x,y) and the base is the region bounded by…

Q: Ex. (8) Sol Solve [D²-6D+9] y = 54x+18 k

A: Given differential equation is (D2-6D+9)y = 54x+18

Q: 4. A 2 kg mass is attached to a spring whose constant is 6 N/m, and the entire system is submerged…

A: Given: X(0)=2-4 ∴2-4=C1-11+C2-131 2=-C1-C23,    -4=C1+C2 The required solution is…

Q: Find sec42x -dx tan 2x A --—-—-cot²2x-—-—-cot³21+ C 16 cot82x) (4sec22x-1) B -(cort2x) 4 12 11 1 C)…

A:

Q: Answer the following problems using the specified method up to four (4) iterations only. Round off…

A:

Q: Determine if the following limit exists: Re(z) + Im(z) lim Z→0 |=|

A:

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A:

Q: Calculate S(102, 100) and s(5, 2) where S(p, k) is the Stirling number of the second kind and s(p,…

A:

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: Explain why you think the series Σα 1 n-1 converges to a finite number or n+1 diverges. If the…

A:

Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

A:

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: Given: Properties of a function f(x) are given below, To find: Relative maximum points, relative…