1. This graph represents the reciprocal of a function f(x). Explain why this graph could NOT be y = 2(x + 1)² − 3 and state the equation of f(x) for which the graph does represent the reciprocal of f(x). -5-4-3-2 7 5 पं 3 2 1 -3 1 2 3 4 5 AR

Q: If (2+3) is one of the roots of the equation x² + (α-ix+bi=o find the valus of a b

A: given  one of the root of the equation x2+(a-i)x+bi=0 is 2+3i we have to find the value of a, b…

Q: 2. Let a, b € Z, where a > b and a 0. Show that there exist integers q and r such that a = bq+r,…

A: Introduction: The well-ordering principle is the basic and very significant property that is…

Q: Find all real-valued solutions to the following differential equation: 16x(5) (t) + 8m²x"" (t) + ¹x'…

A: As per the question we are given a fifth order linear homogeneous differential equation as :…

Q: (a) y' = = ing 3t²y y+1' are probler y(2) = 1 biems

A:

Q: Use Euler's formula to write the expression -2+8i in the form a + ib. Round a and b to four decimal…

A: We will use eulers formula     e^(ix)=cos(x)+i sin(x) to write the given expression in the form…

Q: Find the general solution to the equation y(4) — 14y" + 49y″ = 0. NOTE: Use C₁, C2, C3, and c4 as…

A: Given differential equation is y(4) - 14y''' + 49y'' = 0

Q: 7. A recent published article on the surface structure of the cells formed by the bees is given by…

A: Given function is S=6 lh -32 l2 cotθ +332 l2 cscθ Here, S is the surface area, h is the height and l…

Q: Find the power serious in the power of x.(2x^2-3x+1)y''+2xy'-2y=0

A: Given differential equation is 2x2-3x+1y''+2xy'-2y=0         (1) Let the solution be y=∑k=0∞akxm+k…

Q: Prove k k+1 1 Vnk €N+, ΣΠ(+3) Σ(Π«+») -))) = x + 2 II (~ + i) Π(n k i=0 Here, the meaning of II is W…

A:

Q: 2. Let A Ø. If A has exactly n elements, then A has exactly 2" subsets, Vn € N.

A: We have to prove by mathematical induction : For a nonempty set A, if it has 'n' elements then A has…

Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

A: Consider the given diagram, The equation of the line is given as, y-1=8-135-0x-0y-1=15x-0y=15x+1…

Q: Needed

A: We solve given ODE.

Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

A: solution : let x and y are odd integers . Therefore , we can write x=2m+1 and y=2n+1 for some…

Q: n=1 -7 about the point zo = -3i. Specify the region of validity. 1 6. Calculate the Taylor series of…

A: The Taylor's series of the function fz about the point z=a has the representation ∑n=0∞ anz-an,…

Q: M 2 • (B²+1) y = cos x Ans: y = C₁ C3 x + C₂ sinx + = - =— cos2x spome

A:

Q: the function... f(x)..=. X CX < = TT-X <x<TT

A:

Q: Evaluate the surface integral of D enclosed by the rectangular parallelepiped formed by the planes x…

A:

Q: 3 (6) In a certain state license plates are formed by choosing 2 letters followed by 4 digits…

A:

Q: Using this equation: dt² + Rdq + ²q = E(t) Solve for the equations of current and charge using the…

A: Given equation is Ld2qdt2+Rdqdt+1Cq=Et Substituting the values given 0.001d2qdt2+100dqdt+11q=9

Q: An undamped mass spring system is modeled by the differential equation y" + 100y = 0 a) Convert the…

A: a. Given differential equation is y''+100y=0 Let x1=yx2=y'=x1' So, x2'=y''=-100y=-100x1+0x2 So, the…

Q: Rewrite - 1 sin(x) - 4 cos(x) as A sin(x + ) A = Note: should be in the interval -π << T

A:

Q: -t 9-y" + 2y +y = 3e¯t

A:

Q: Consider the family of curves: y² - 2x² = cy. A) Describe this family geometrically (e.g., "circles…

A: It is provided that: y2-2x2=cy. We need to describe this family geometrically. We also need to…

Q: the function f (x, y) = xy2 +1/6 x3 − X + 1 is given. a) find and classify all critical points of…

A: Let us consider the given function f(x,y). Determine the critical points. Find the partial…

Q: 2. A manufacturer is studying the effects of cook- ing temperature, cooking time, and type of…

A: We have to find Answer only the problem (2) as said in the Question.

Q: 2) Solve for x (give your answer as an integer between 0 and 9): 51 + 27 ≡ x(mod10)

A:

Q: Prove n k Vnk €N+, Σ (Í[6+5)) = i=1 Here, the meaning of II is j=0 n II = ¹ 1.2.... i=1 .n k+1 1 k+2…

A: As per the question we have to prove the given identity involving nested partial sum and partial…

Q: Consider linear transformation F: R4 → R³ given by a) b) c) d) F(w, x, y, z)=(w-3x+2y-z, x−y+z,…

A: Given :  F : ℝ4 → ℝ3 be a linear transformation defined as ;             F(w, x, y, z) = (w-3x+2y-z,…

Q: A store has determined that the number of Blu-ray movies sold monthly is approximately n(x) =…

A: It is provided that n(x)=67500.928x. We need to determine the revenue function, profit function. We…

Q: Solve the y" + 5y' + 4y = x²e²x following CDES by variation of parameters method

A:

Q: Suppose f(x)=√x is to be approximated near x=8. Find the linear approximation to f at x = 8. Then,…

A: In this question, the concept of linear approximation is applied. Linear approximation of fx at x=a,…

Q: Problem 2 Write the sentence with variables p, q, r and connectors, A, V for the following two truth…

A:

Q: Define the binary operator ★ by: a+b= a +8b Find each of the following: a. 2*5 = b. 4*4= C. c. 5 + 2…

A: Binary operation:  Binary operation * on a set S is an operation, when applied to any element x and…

Q: 5. Prove that if x, y € R, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: Properties of inequality If x,y≥0 Take x=k, y=m, k,m is positive f x,y&lt;0 Take x=-k, y=-m, k,m is…

Q: use the biomal series (x + 1)k = 1 + kx + or || < 1 to approximate [¹ k(k − 1) 2! -x² + k(k-1)(k −…

A: Given : x+1k =1 +kx+kk-12!x2+kk-1k-23!x3+......    x&lt;1 To find  :∫01x42+1dx

Q: 6. Determine the Fourier integral representation of the following: 0 < t < 1 elsewhere t, f(t) = {t

A: Given function is ft=t0&lt;t&lt;10elsewhere So, the Fourier integral representation is…

Q: Prove the following by mathematical induction. V4 ≤NEN, 2n<n!.

A: We have to prove ∀ 4⩽n∈ℕ,  2n&lt;n! using mathematical induction.

Q: Consider the data set below: 35,24,25,38,31,20,26,28 Which of the following box-and-whiskers plots…

A: We have a data set 35,24,25,38,31,20,26,28 Now,  minimum = 20maximum=38 Arranging the data in…

Q: Using orthogonal invariants, determine the type of the second-order curve and find its canonical…

A:

Q: 2. Let a, b € Z, where a > b and a 0. Show that there exist integers q and r such that a = bq+r,…

A: Let a=28b=5 The we can write 28=55+3 So, we have proved the statement.

Q: S&L Financial buys and sells securities expecting to earn profits on short-term differences in…

A: Trading securities are recorded in the books at their fair market values. Cost of Coca-Cola bonds =…

Q: 4. Explain how you know this is NOT the graph of the reciprocal function of ƒ(x) = (x − 2)². ✔ T 7 5…

A:

Q: 9. 10. 2ss" + (s')² = 0 2ste tds +(s²e-t-t)dt = 0

A: As per our guidelines we are supposed to answer only first question . Kindly repost other parts in…

Q: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

A:

Q: Q.3 Under what conditions on A and B does the B.V.P x²y"-3xy' + 3y = e³x cos 7x, have exactly one…

A: Introduction: The solution of a boundary value problem depends upon the boundary conditions.…

Q: In problems 3 and 4, use Lagrange Multipliers to find the maximum and minimum values of f subject to…

A:

Q: Question 1 what is the easiest Maclaurin. Question 2. way. to find Series for the function. f(x) =…

A:

Q: Find the Wronskian of the given pair of functions: X O x² et O xet i, xet

A:

Q: Use the intermediate value theorem to classify each function according to the existence of zeros on…

A:

Q: Given n ≥ 3 circles on the plane, satisfying • Each two circles intersect at exactly 2 points; . No…

A: Given: for n≥3 circles on the plane, every two circles intersect at exactly two points and No three…