Let f(x) = -4x+ 2. Find the largest & so that f(x) - f(a)| < e when |x-a| < 8. S .

Q: What is the equation that represents the Volume of the box as a function of the cutsize of the box?…

A:

Q: Let I = {(a, 0) | a ∈ ℤ}. Show that I is a prime ideal, but not a maximal ideal of the ring ℤ×ℤ.

A:

Q: Using ordinary interest, 360 days, calculate the missing information for the simple discount note.…

A:

Q: (c)(i) Use the substitution x = tan²0 to show that √x 。 (1 + x² ) ² (ii) Hence find in simplest…

A: We have to show                            ∫01x1+x22dx=∫0π42sin2θdθ     by substituting  x=tan2θ and…

Q: Prove or disprove: The image of a PID under a homomorphism is a PID.

A: Introduction: PID:  Every appropriate ideal may be created by a single element in an integral domain…

Q: 3 days? (Write

A:

Q: 37x = 101 (mod 151)

A:

Q: 1 (a) Is Σ 1 n n+1 n=1 plain your answer! conditionally convergent or absolutely convergent? Ex-

A: Series and sequence, telescoping series

Q: Answer TRUE or FALSE. Along with your answer, provide a proof if true and a speci c counterexample…

A:

Q: 16 When absolute risk is low, it is often reported as the number of cases per 1,000 people, per…

A:

Q: Here's a trickier example of a subgroup of GL(2, R): sin o 6)}~{( *)} cos d o sin cos o K= sin cos…

A:

Q: At time t=0, a particle is located at the point (1,3,1). It travels in a straight line to the point…

A: according to question,  initially the particle is at point 1,3,1 then travel to point 7,8,9 in a…

Q: 1 3cotx expression in terms of one function: 3tanx -

A:

Q: A. Determine whether the given is an exponential function, an exponential equation, an exponential…

A: Part (A):- Given information 1.  fx =7-x2.  7&lt;343x-23.  fx =x2+1

Q: If H is an infinite dimensional Hilbert space, then prove that every isometric isomorphism of H onto…

A:

Q: When asked the question "what is time?", the fourth-century Christian philosopher St. Augustine…

A: The Given statement is "If you don't ask me, I know, but if you ask me, I don't know" Let us define…

Q: 6. Model radioactive decay using the notation t = time (independent variable), r(t) = amount of…

A:

Q: Examples. Justify your answers briefly. (a) Suppose that real functions f and g have the same value…

A: It is given that, real functions f and g have the same value on some open interval containing 0.…

Q: Examples. Justify your answers briefly. (c) Let S be the set of points (x, y) in R² so that x² + 4y²…

A: (c) It is given that S be the set of points (x, y) in ℝ2 so that  x2+4y2 = 1. We have to explain…

Q: Calculate the volume of the following systems by setting up the triple integral. Draw the volume and…

A:

Q: 1. For any integer n, the quantity 3 (n² + 2n + 3) - 2n² is a perfect square.

A: We need to show that for any integer n following quantity is a perfect square: 3(n2+2n+3)-2n2

Q: Suppose a package in the shape of a rectangular box can be mailed by a ceratin postal service if the…

A: Answer :-

Q: proof *without* using the eigenvalues? Please use the facts that a positive definite matrix A…

A:

Q: Consider the groups Z[i] = {a + bi | a, b = Z, i² = -1} and Z (both under +), and the function o:…

A:

Q: 5. A bag contains 20 identical red balls, 20 identical blue balls, 20 identical green balls, and one…

A:

Q: Obtain the particular solution when x = -1 and y = 0 1 (2x + 3)dy = ydx + (2x + 3) dx

A:

Q: ) Find a nonzero vector v with v € Span {0.0} 2 [1] [12]) and

A:

Q: Solve the linear programming problem by the method of corners. Minimize C = 7x + 6y      subject to…

A:

Q: Exercise 2. Unlike real waves, complex waves can have negative frequencies. In terms of the circle…

A: We are given the following. The notation eiθ instead of cis(θ). Exercise 2: Unlike real waves,…

Q: Let a be any number from R, and let b be a number from R that is positive. The solution interval to…

A:

Q: 1. Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A:

Q: ∞ (a) Is Examples. Justify your answers briefly. B÷-1²1) n n+ n=1 plain your answer! conditionally…

A:

Q: Third Derivative The third derivative of a function f(x) is the derivative of the second derivative…

A:

Q: a Let Z[√2] = {a+b√√2 | a, b € Z} and let H = { b Show that Z[√2] and H are isomorphic as rings. 2b…

A:

Q: A scale drawing of a football field has a scale of 1 inch to 40 feet. The area of the scale drawing…

A:

Q: How would I prove (or disprove) the following: every onto function f: Z → Z also one to one? (where…

A:

Q: Refer to the following statement to answer parts (a) through (c) below. The mathematician is…

A:

Q: Find a basis of the eigenspace associated with the eigenvalue -3 of the matrix A Answer: -2 -1 1 0…

A:

Q: K4,4 Multiple Choice . . . . ܩ ܦ ܕ ܕ . ܘ

A:

Q: (5) Let A be an mxn matrix. The row space of A, denoted rowspace(A), is the span of the row vectors…

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A: For any non zero vector u→ if we divide by length of this vector then it will becomes unit vector in…

Q: Complete the truth table for the given statement by filling in the required columns. -pv-q Pq Р TT T…

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

Q: (b) (c) (d) (e) dy=3x²(y-1) dx dy_y+2 = dx x+1 dy dx -+e*y² = 0 dy dx -= cos x tan y hotnes

A:

Q: An investment grows according to the formula B = 6000 x 1.0065 dollars, where t is time, measured in…

A: An investment grows according to the formula B=6000×1.0065t dollars where 't' is time (in months).

Q: Show that if A and B are n x n matrices then N(A-B) = R" if and only if A = B.

A:

Q: Show that every element of GF(pn) can be written in the form ap forsome unique a in GF( pn).

A: In this question, we have to show that, every element of GF(pn) can be written in the form ap for…

Q: How to prove the following: if A ⊂ image f then f(f -1(A)) = A.

A: The details are given in step 2.

Q: Can anybody review this, and maybe submit it in a format that can be followed?  The response should…

A:

Q: A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It…

A: First of all let's consider the constraints/limits on the values for x and y: x≥0 and y≥0 since it…

Q: How much more would you earn in the first investment than the second investment? $49,000 invested…

A: