Prove the statement using induction. 1² +22+3² +4² + ... + n² = If n € N, then If n ≤ N, then ++ +· n(n+1)(2n+1) 6 1.2+2·3+3.4+4.5++ n(n + 1) = n(n+1)(n+2) for every positive integer n. n (n+1)! 1. (n+1)!*

Q: curve equations of principal normal and x = 4a cos³ 0, y = 4a sin³ 0, z = 3c cos 0. Find the…

A:

Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

A:

Q: f(x) = 3x2 + 2x - 5 then f(-2) =

A:

Q: A fair dice is thrown three times. If p, q and r are numbers obtained on the dice, then find the…

A:

Q: Give three equivalent properties of conservative vector fields. Consider the vector field F defined…

A:

Q: The demand for flatscreen TVs is P= 1,300 - 50QD- The supply of flatscreen TVs is P = 750+20Qs- What…

A: Given demand for flatscreen TVs is  P=1300-50QD⇒QD=1300-P50 Given supply for flatscreen TVs is…

Q: X x + 1 (a) State the domain of the function. 3. Let y (b) Find all asymptotes. State the behavior…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 8. Given f(x) = - 2 log₂ (6-2x) + 3 a) Determine the following information; show your calculations.…

A:

Q: 3. 4. 5. t2 sin 3t-3t cos 3t 2 sinh 6t-4t cosh 6t 1²e-2t sin 8t

A:

Q: TP-4 Find the volume of the solid that lies below the paraboloid z = 4 - x² - y², above the…

A:

Q: 20. Using = 00 1-x n=0 a) Find a power series for c) Find a power series for 1 1+x¹ - 4x³ (1+x¹) ²…

A: The given problem is to find the power series of the given functions with using the given power…

Q: Compare the values of the series 2 n1.4 A = Σ n=2 and the improper integral B = 1. AB 2. A B 3. A B

A: Given: There is a series A = ∑n=2∞2n1.4 and an improper integral B=∫1∞2x1.4dx Our aim is to compare…

Q: Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the…

A: Given vector field is: F=7y, -9x To Do: (a) Calculate the curl of F. (b) Calculate the divergence of…

Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. 5- 1 2 3 4 5…

A:

Q: Consider the 15 × 15 Hilbert matrix H. You can construct this matrix using the matlab command…

A: You can construct a 15 × 15 Hilbert matrix by using the command hilb(10). We will write a matlab…

Q: Which one is the solution to the given iterated integral? (Hint: polar coordinates) L'S√²-²…

A: We have to find the value of given double integral.

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: 12. Answer these questions about the rooted tree illustrated……. (a) Which vertex is the root? (b)…

A: For the given rooted tree we have to find: (a) The root vertex. (b) The leaves. (c) The children of…

Q: In fall 2014, 36% of applicants with a Math SAT of 700 or more were admitted by a certain…

A: Solution:-

Q: Surface Integrals ( surfers of th unit Let S be the sphere centred at onlin. outwards) @ find a…

A: The given surface is, x2+y2+z2=1. (a) To Find: A vector field F such that ∬SF·dS<0. (b) To Find:…

Q: Use Newton's method to approximate a root of the equation 3x7 + 4x + 2 = 0 as follows. Let x₁ = 1 be…

A:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: Solution :-

Q: Evaluate the surface integral F ds for the given vector field F and the oriented surface S. In other…

A:

Q: a) F(x, y) = (x + y)i − (x² + y²)j around and across the triangle bounded by y = 0, z = 1 and y = x.…

A: To find the circulation for the given vector function by using Green's theorems.

Q: Packing Flower Pots A gardening company sells clay flower pots and plastic flower pots. There must…

A:

Q: Q17. Suppose M is a stochastic matrix representing the probabilities of transitions each month.…

A:

Q: Pontificis fait now. PT 00 Р T F F q T FT O Tautology F O Contradiction -P FL F T T LL Determine…

A: This question from discrete mathematics.

Q: m η In Tutorial we prove that Σ1Σ1ΐy; = ΣιΣ=1&ty; = 4 of the steps of the proof in Tutorial (and…

A:

Q: 2. a) Answer True or False. Justify your answers. {2,33 € {1,2,3 {1,333 {1,23 CE₁, E23, 3, E1, 233…

A:

Q: Find the volume (in ft³) of the gravity bin the figure below. (Use the rules for working with…

A: Solution:-

Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

A:

Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

A: We have to check whether given vector field is conservative or not.

Q: 25) (-1)+¹((n + 1)² − n²) n=1

A: Solution:-

Q: 27) (1-1) (Hint: (1-²)→ Ỹ n=1 N.N →1/e

A: Solution given below.

Q: Please answer all

A:

Q: Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u, v)) for the following…

A:

Q: (a) Complete the Intermediate Value Theorem: If f is continuous on an interval I, assume that a, b €…

A: Solution is given below.

Q: Use Newton's method to approximate a root of the equation x³ + x + 3 = 0 as follows. Let x₁ = − 1 be…

A: Given that:  x3 + x + 3 = 0 f(x) = x3 + x + 3 x1 = -1 Now, differentiating the f(x)  We get, f'(x) =…

Q: Find a power series representation for the function rsin(5) on (-00, 00). α 1. f(x) = Σ (-1)"-1 n=1…

A:

Q: For the series below calculate the sum of the first 3 terms, S3, and find a bound for the error.…

A:

Q: =rs obtained on the dice, then find the probability that + i = 1, where i = √-1.

A:

Q: Apply properties of congruence to make computation in modulo n feasible. Find the unique r such that…

A:

Q: Let DE M₂ (R) be idempotent that is different from the identity and zero matrices. Show that the…

A:

Q: Define Jn(x) = x²n+¹In(x), for n ≥ 0 Exercise 2.1: Use the facts that Jn(x) 1)In-1(x) - An(n-1)…

A:

Q: 3 [x³ (2+x¹)³dx

A:

Q: Let f(x, y) (x, y) = (0,0) 0 (x, y) = (0,0) , derivatives exist at (0, 0) but the function is not…

A:

Q: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant…

A: A company manufactured two types of skis: Trick ski and Slalom ski. A table is given that represents…

Q: 1.38, for a poder of the care of intersection of the worffeet Beredar A BINTI CONTE B

A:

Q: Use laplace transform to solve the initial value problem: 3rd order IVP : 11 y + 24" y' - 2y = sin…

A: Given the differential equation y'''+2y"-y'-2y=sin3t. After applying the Laplace transforms,…

Q: Find the orthogonal complement S+, and find the direct sum se st. -{8} (a) Find the orthogonal…

A: