(a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ + 27)*. %3|

Q: Evaluate the integrals in the following questions using integration by parts For 0 cos T0 de

A: By Parts Rule: ∫u(x)v(x) dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Evaluate the summation 7-i. 22 25 18

A:

Q: + 2x-3 Find a lim f) b lim , x) Jig. f(x) d lim rx)

A:

Q: cln2 e-x dx 0.

A:

Q: 19) y"- 4y'+5y= 0, y(0) = 1, y'(0) = 2.

A:

Q: 13) y"+7y'+12y = 21e", y(0) = 3.5. y'(0) = -10.

A:

Q: In (x + x²) dx

A: Given problem:- ∫ ln(x+x2) dx

Q: loof yadT h 5: A party planner is trying to hang a sign between a house and a palm tree for…

A:

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A: In a particular very small region, the consumer price index, C, depends on the current value of…

Q: Suppose 200 trout are seeded into a lake. Absent constraint, their population will grow by 70% a…

A: Given problem:- Suppose 200 trout are seeded into a lake. Absent constraint, their population will…

Q: 5. S (16z³ – 14x + 6) dæ

A:

Q: | cos 3x cos 4x dx :

A:

Q: Sco cos 3x cos 4x dx :

A: Use simple integration formula.

Q: | csc² 20 cot 20 de

A:

Q: 27) y"+2y'+ y = e", y(0) = 0, y'(0) = 0.

A:

Q: -3 0 5] 1-3 0 5 18) 00 0 1 1 00 0 0 0 A) 5 B) 4 C) 3 D) 2

A: Consider the matrix

Q: (y In a In y) dr + dy = 0 O In In y| + x Inx +x = C O In y = Ce" r* O y = eCe*z* O y = eCe*z ts)

A:

Q: Determine the Laplace transforms of * 3, 7 12

A: Determine the Laplace transforms

Q: Evaluate the integrals in the following questions using integration by parts for In (x + x²) dx

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: answer

A: Please refer to the image below

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

A: Apply Lagrange multiplier

Q: Find the series' radius of convergence E (3x)n n=0 O1 00 O 3

A: This question is related to infinite series, we will solve it using given information.

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

A:

Q: 6 Evaluate the limits lim: X+ co X 6.

A: Topic:-   limits and continuity

Q: 4. S Væ*dx

A:

Q: 7 7 = 3, f(x)dx = 8, and g(x)dx = 5. Evaluate the following integrals. Sowar=s. 2 2 2 Sawak = -5 7…

A:

Q: How many ways are there to distribute r+s identical balls among five different children such that…

A: We need to find ways to distribute balls as asked.

Q: |cos 3x cos 4x dx :

A: We have to find the given integral.

Q: Find the area under the graph of the function over the interval given. 13) y =ex; [-9,4] A) e 13 B)…

A: We can find the area as below.

Q: Find out all the relative minimum and maximum values, and sadle points of the function h defined by…

A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

Q: Find critical points of the function e(2 -3x) O x = 0, x = 1 O x = 1, x = 3 O x = 0, x = 2 O this…

A: Topic = Derivative

Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…

Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

A:

Q: Solve the initial value problem (3+x2)y/" + 4y = 0, y(0) = 0, y (0) = 12. |3D If the solution is y =…

A: Please see the below picture for detailed solution.

Q: 1 е. (s2 +1)(s2+4s+8)

A: This is a problem related to laplace transform. Based on the partial fraction decomposition and…

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

A:

Q: The area of the base of a rectangular prism is equal to the area of the base of a cylinder with an…

A: The area of the base of a rectangular prism is equal to the area of the base of a cylinder with an…

Q: (b) Find the values of a and b so that the function f(x) = x2 + ax + b has a local maximum at the…

A: f(x)=x2+ax+b

Q: In finding the area underneath a curve, which among the Riemann sums and definite integral is the…

A: Riemann Sums : As we know that a Riemann sum is an approximation of a region's area, obtained by…

Q: 3. J

A:

Q: 1. Consider the figure below. y=4x VEx+2\

A: Explanation of the answer is as follows

Q: Consider the function defined by 1 g(x, y) = cos (Tx Vy) + log3 (x – y) Calculate the instantaneous…

A:

Q: Find the equation of the plane passing through the three points A = (-1,0,2), B= (2, –1,2), C = (3,…

A: Given problem:- Find the equation of the plane passing through the three points A = (- 1, 0, 2) B =…

Q: xdx Trigonometric Substitution -4x-7

A:

Q: Determine whether the series converges or diverges. Σ n2 + 5 n = 1 converges O diverges

A:

Q: Using integration, derive the Laplace transform of: * L(sinh at)

A: This is a problem related to integration. based on the general formula and concept we will answer…

Q: Evaluate the summation 5/32 31/32 93/80

A: This question is based on summation.

Q: A. Evaluate the following integrals. 1. S(Vcosx + sin x)*dx 2. S cos³ 3x dx 3. S tans 2x dx

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Tx VT) + log3 (x – y)" Determine

A: We can solve this as follows: