10. The expression sin (32) cos (22) - cos (32) sin (22) is equal to

Q: 3 2 Given f'(x) = 2x³ + 2x² + 3x, f(x) has: a. 1 critical point b. 3 critical points c. 4 critical…

A: We have to find the critical points

Q: Find the given determinant by any method. 0000-91 000 20 00-70 0 040 0 0 50000

A: Given matrix, A=0000-90002000-7000400050000

Q: A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C…

A: To explain with the examples with the algebraic vector properties given.

Q: (3x² - 10)dx x² - 4x + 4

A: The integral using substitution is answered below:

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

A:

Q: Evaluate using Partial Fraction Decomposition: (- dx

A:

Q: x(t) Find the point at which the line y(t) z(t) = 6+t -8 5t intersects the plane. 7 + 2t

A: SOLUTION-

Q: 2. Show the volume of the solid obtained by rotating about the x-axis the region 1 under the curve…

A:

Q: For the function f(c)=3x^4-8x^3-48x^2+1 A) find all critical numbers for B) on which intervals is…

A: Using critical point find intervals in which function increasing and decreasing

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: let  x, y, z  be the non zero  vector that is orthogonal to   u, v and w

Q: 4dx 3 x - √√x² S

A: We will use simple Integration rules to solve this question.

Q: Consider the region bounded by y = ²+1, y = 1, and y-axis. Using the Cylindrical Shell Method, which…

A: The given bounded region is as shown below; Apply the cylindrical shell method to find the volume…

Q: If dx = e-²y and y = 0 when x = 5, then the value of x when y = 3 is dx e6 +9 A. e5 C. 2 B. e6 + 1…

A:

Q: Iff and g are differentiable functions and h(x) = f(x)ex) , then K'(x) = rosen Fixe+fixie O [00+0000

A:

Q: Determine the area to the left of x = 3- y² and to the right of x = -1

A: See the details solution in below

Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

A:

Q: The x-component of a force of 50N is 30N, then what will be the y- component of the same applied…

A:

Q: 4) A tank contains 100 gallons of pure water. A brine solution with 1kg/gal of salt enters at…

A: Let's find amount of salt in the tank after 45 minutes.

Q: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

A:

Q: What is the domain of the function f(x) = |x|? 0 (-∞,∞) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

A:

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

A:

Q: 13. Given - 5x + 5z = a. (-5, 5, 2) 2, the normal of the plane is: b. (7, 7, 0) c. (-5, 0, 5) d.…

A:

Q: My - Nx If = =Q, where Q is a function of x only, then the differential N equation M + Ny' = 0 has…

A:

Q: Get a similar question = y = 5√x. and the change in y, Ay when x = 2 and Ax = 0.2 nd the…

A:

Q: Use the transformations to graph the given function. Show all translations on each transformation.…

A:

Q: Consider the following equation f(x)=x²-2x+2 whose roots we seek with an initial guess of x-4. Fixed…

A: We have to find the correct option.

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

A:

Q: dx 4-9x²

A:

Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

A:

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

Q: Given the following vector field and oriented curve C, evaluate SF.T ds. C F= (-3y,3x) on the…

A:

Q: Which of the following statements is (are) true? I. If f is a function from [a, b] to R and F is any…

A:

Q: Which of the following is a mathematical sentence? 1.2 is a prime number. II. = 0. I and II Il only…

A: To find out the correct option.

Q: Solve the following integrals: 1. S-7e*dx 2. (2ex - 6x) dx √² (3x) dx 3.

A:

Q: Solve for y esec(4y²-6y+14) = 3x + 1

A:

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: 2 dydx -23-1 (xy)³ SS.

A:

Q: Question 6 Find two numbers whose sum is "a", if the product of one to the square of the other is to…

A: Using algebraic operation

Q: Find the determinant of the following elementary matrix by inspection. [0 100 1000 E = 0010 0001…

A:

Q: 1 Consider the function f (x) = on the interval X - 1, 1]. If the Mean Value Theorem can be applied…

A:

Q: (2x²9x9)dx x3 x³ - 9x

A: Here we have to do partial fraction and after that integration

Q: an+1 Use the ratio to determine if the an +∞ n sequence {zn is strictly 2n + 5Jn=1 increasing or…

A:

Q: - Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x) -1(y/x)

A:

Q: f(x csc² 6x-x cos 6x)dx

A: Given,∫ (xcsc26x-xcos6x)dx

Q: A rectangle is bounded by the x-axis and the semicircle y = √25-x² What length and width should the…

A: Area of a rectangle is the product of its length and width. We use first and second derivative test…

Q: A container with square base, vertical sides, and open top, is to be made from 3,000 ft² material.…

A: This question is based on application of derivative.

Q: By using Chain Rule, find au/ax, au/ay, du/az at (x, y, z)=(√√3,2,1) U= P-q q-r p= x+y+z q=x-y+z,…

A:

Q: 11. Given x = 1 + t, y = 6, z = 3t + 7, the direction vector of the line is: a. (1, 0, – 3) b. (1,…

A: