Use Lagrange Multipliers to solve the following: Maximize f(x,y,z) = 4x + 2y + z subject to x^2 + y + z^2 = 1.

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

A:

Q: Express the following sum.. using sigma notation. 1 d. 9 1 Σ 12 + + + 10 11 k= 1

A:

Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

A:

Q: graph below, whet is a pont ad which it would O Giue the function in the reas ona ble estimete…

A: The inverse function is reflation to original function at y=x

Q: Consider the function f(x) = x* + 2x'. (a) Find the x- and y-intercepts of the graph of f (if any).…

A: Use derivative for finding the extreme point.

Q: S16 sin²x cos"x dx the solution is 2x 4 sin x cos x +2 sin x cos x +C 1 x- 2 sin x cos x + 4 sin x…

A:

Q: Evaluate the integral by interpreting it in terms of areas •5 (x – V 25 – x?) dx -5

A: Given,  ∫-55x-25-x2dx

Q: -4 Determine the limit: lim -i (и — 1)2

A:

Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…

A:

Q: Find the divergence of the following vector field. F= (3xyz, - 2xy z, - 4xyz?) %3D The divergence of…

A:

Q: V 192 °

A:

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

A:

Q: lim [f(x) – (x + 1)] = 0 • f is R\{2, –2} • f(1.5) = f(3) = 0 continuous • lim f(x) = -∞ on lim…

A: Given:-   To find:- Determine the intervals where the graph of f increasing/decreasing and concave…

Q: (x)dx = (Type an integer or a simplified fraction.) a

A:

Q: For the function shown bellow; Find the second order derivatives : af/ay (a^2 f)/(ay^2) f (x, y) =…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

A:

Q: e3 1 - Find lim

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the minimum and maximum values of the function y = 1613 + 24t² on [1,2] by comparing values at…

A: Explained below

Q: ravels down a highway at 50 m/s. An observer stands 250 m from the highway. w fast is the distance…

A: Topic:- geometry

Q: Suppose that k(x) is a continuous function defined on the domain 0 sxs5 and is graphed to the right.…

A: Critical points are defined as those points where the derivative ia either zero or infinity.

Q: Find the minimum and maximum of the function y = z° – 6480z on [-8, 8] by comparing values at the…

A:

Q: •1//2 4 c) dx. VI – x² 1/2

A: To evaluate the integral.

Q: I. Evaluate the following. You are NOT allowed to use L’Hopital's rule. Vx² – 2x – 3x 3 - V11+ 4x 2x…

A:

Q: For | cos 3x cos 4x dx :

A:

Q: n lim (5(x;) – 3(x;)*)Ax over [0, 2] i=1

A: To convert this limit of sum as definite integral over given interval.

Q: d'y (3x* – 5)(2.x² +9x–6) Determine the of y = 3 dx 7x

A:

Q: 5t4 dt Vto +2

A:

Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y"…

A:

Q: Find an eigenbasis and diagonalize. (Show the details.) 101 72 9. -144 -103.

A:

Q: Convert the equation to polar form. (Use variables r and 0 as needed.) x = y

A: Given :x=y

Q: Not yet answered Marke Prove that f(x) = (x- 1) + (x +1)² is an even function. A function k(x) is an…

A:

Q: A curve is defined implicitly by the equation ax + by2=r2 Given that a=20, b=2 and r=7, find the…

A: We have to find the solution.

Q: Write the sequence in recursive form. Make sure to state the initial conditions a, - 4(3)" for n > 1

A: Solve the following

Q: Obtain the general solution unless otherwise instructed 2. у" — у' — х — 0 SUMMARY OF ANSWERS 2. Yc…

A:

Q: 3 B. Find the eigenvalues. -. 2,= -1 & 1z= 4 B. A,= 2 & 12= 2 C. A,= 4 & 12= 1 E Nona

A: Topic:- matrix algebra

Q: The following series is convergent: 3n 2n? – 1 Σ 4 + 5n2 n=1 Select one: True O False

A:

Q: Find the first 5 terms of the following sequence and then write the sequence in list form. b 26 –1 –…

A:

Q: In (x + x²) dx

A: Given problem:- ∫ ln(x+x2) dx

Q: The series 2 + Vn2 1+ Vna n=1 is convergent if and only if: Select one: O a. a > Ob. a Od. a < O e.…

A: As per guidelines we have to solve one question Please repost other questions again

Q: Evaluate the following: 1. f (5a - 82 + 6z² - 4x + 7) da

A:

Q: Use the figure to find the exact values of sin(2u), cos(2u), and tan(2u). sin(2u) cos(2u) tan(2u) II…

A:

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by variation of parameters…

A:

Q: 7. y = csc csc (3x – 1) 8. y = 3secx + 45

A: Solving

Q: for In (x + x²) dx

A:

Q: Express the following sum using sigma notation. a. 7+8+9+ 10 + 11 5 a. 7 + 8 +9+ 10 + 11 = E| k=1

A:

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

Q: If 2n+3 a %3D 5n+8

A:

Q: Use Riemann Sum to find the area bounded by f(x) and the x – axis: f(x) = 4 – x² over [-2,2] x =…

A:

Q: 3. y = xcos(2x) 4. y = tan tan (3x)

A: To find out the derivative of the function.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: