The sum of two positive numbers is 16. Find two numbers such that the sum of the squares is a minimum

Q: Let f(r) = x³ on [0, 1] and let Pn be the arithmetic partition that splits [0, 1] into n equal…

A: Given

Q: - SCx³ – 2x²) (÷ – 5) dx

A:

Q: Which of the following parametric functions create this graph? -4- -2- -2 2 -2 -4. x (t) 4 cos(t)…

A:

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: Consider the points A(3, –3, 3), B(4, –5, 1), C(-2, -4, 1), and D(6,3, –5). |(a) Find the volume of…

A: Let's find.

Q: 2 * - 3 dy 4. S 1 y +y 2

A:

Q: S 4x* sin2x dx A (2xª + 6x² + 3) cos 2x + (4x³ + 6x) sin 2x + C C (2xª – 6x² • 3) cos 2x + (4x³ –…

A: Integrating by parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx dxndx=nxn-1 ∫cos(ax)dx =1asin(ax)+C ∫sin(ax)dx…

Q: Evaluate the iterates integrals r*dA D = {(r, y) : 1 <I< e, 0Sys In(r)}

A: Given problem:- ∫∫D x3 dA        D={(x, y) : 1≤ x≤ e, 0≤ y≤ ln(x) }

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: We will create a Lagrange's function to solve the problem.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 4j as…

A:

Q: integrate the following:  Ue the U-substitution. ∫3/(√4x2-12x+9) dx

A:

Q: Find the relafive maximam/minimum values of the Fuction F(x)=X-2 State where the functian is…

A:

Q: Determine whether each improper integral below converges or diverges. dx 3. S 0 x* + 2x – 3

A:

Q: Find the relative maximam/minimum values of the fuction てキX Stak where the Function S increasing of…

A: For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A:

Q: For demand function d Q = a −bP and supply function s Q = dP − c , using Cramer’s rule determine…

A: For demand function d Q = a −bP and supply function s Q = dP − c  Using Cramer’srule determine…

Q: 1) cos(s*)dtds

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A:

Q: x sec (3x) tan (3x)dx

A:

Q: S(3x2 — х + 2) е -* dx | A - (3x2 – x + 2)e* (бх 1)e * + 6 e¬* + C (-3x² – 5x – 7)e¯* + C (3x? —х+…

A:

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

A:

Q: Evaluate/Find the following integrals. 2 4. S2-3 3 -dy 1 У +у 2

A:

Q: C Solve the following problems. 16. What value of k makes the function continuous at x= 3? Graph the…

A:

Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

A:

Q: 2 +y? +? inge muitipilers to find the maximum and minimum values of f(x, y) = 2x + y – 2z subject to…

A: We are using Lagrange multipliers method

Q: /4y² - 25 -dy

A:

Q: 6: evaluate öz/du and öz/ðv at the given point (u, v). z = tan (x/y), x = u cos v, (u, v) = (1.3,…

A:

Q: r'dA D = {(x, y) : 1 <I<e, 0Sys In(r)}

A: We need to apply the integral limits appropriately and then integrate it.

Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A:

Q: 8 16 22 63 26 51 75 29 67 LIt rained 35 inches last year. This year, it rained 19 inches. How many…

A:

Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1,–4, 2), and D(4, 1, –8). (a) Find the volume of…

A: Given: A(3,-3,5)  B(5,-5,2)C(-1,-4,2)D(4,1,-8)

Q: Calculate the following sums. (Use symbolic notation and fractions where needed.) 8. (a) i=1 8 (b)…

A:

Q: Vx-2 4. Lim x→2 Vx2-4

A:

Q: I need help with "Determine whether the lines L_1 and L_2 are parallel, skew, or intersecting. If…

A:

Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

A:

Q: Consider the following IVP: Find the general solution. 1. y"-3y'+2y = e3t ; y(0) = 0, y'(0) = 0

A: According to our guidelines, we can answer only one question. Other questions can be reposted.

Q: Use the shell method to write and evaluate the integral that gives the volume x + y? = 16 y 4| 3 2.

A: In this question we will use basic concepts of calculus i.e concepts of volume of solid revolving…

Q: Show that the absolute value function is continuous at x = 0. 2. Show that the signum function is…

A:

Q: 3. Evaluate the following using Integration by Parts, Algebraic Substitution, Trigonometric…

A:

Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

A:

Q: Use seperation of variable to solve the following differential equation (DE): (11 + x) dy – y dx = 0…

A:

Q: I (z sin(x) + y² )dV Evaluate 5 5 B = {(x, Y, 2)|– as *<I<,4 < y< 8,4 < z < 6} . %3D 6. Round your…

A:

Q: Find the directional derivative of f(x, y, z) = 5y at P(5, 1, –4) x + z in the direction from P to…

A: We have to find directional derivatives for the given function.

Q: A closed rectangular box with a volume of 375ft° is made from two kinds of materials. The top and…

A:

Q: Find the area bounded by the graphs of f(x)=x+2, g(x)=3x²+5 , x=-1 and x=1.

A: Explanation of the answer is as follows

Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

A:

Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: (k) (In n)n n> 2.

A: k. 1ln nn ,  n≥2let, un=1ln nnun=1ln nn12=1ln nn2by cauchy roots testlimn→∞  un1n=limn→∞  1ln…

Q: (16030186) QUESTION 3 Use partial fractions to calculate the fol 3x-6x-1 3.1 dx (x²+1)(x+1)(x-1)

A:

Q: Determine if the following statement is true or false. The lines L1 and L2 are skew. L:x = 10 + 3t,…

A: