Find lul, Ivl, 12ul, |2v|, lu + vl, lu − vl, and _|u| - |v|. u= 5i + j, v = 2i - 4j

Q: Directions: Solve the following using the theorems on differentiation. 1. Evaluate | 7e*dx 2.…

A:

Q: f(x) = xlnx

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: Solve the given initial value problem. + xy = 2 ²y² + y² = 3 O xy² + xy³ = 0 xy² − y³ = 1 O x²y² -…

A:

Q: y4 + y² − 1 y³ + y - dy

A:

Q: 1 x √x²+3 igonometric substitution to find f

A:

Q: Find each derivative. f(x) = ln sin x COS X y = cos(x² - 2x-8) g(x)=e-In(cos.x)

A: The answers are given below: Topic : Differentiation using chain rule

Q: Find the characteristic equation, the eigenvalues,

A:

Q: convert the following differential equation into a Perfect equation and then Find its general…

A: Given problem:- convert the following differential equation into a Perfect equation and then Find…

Q: Team Alpha was on their night patrol in Mystical Forest when they suddenly noticed that a flare was…

A: here distance we have to find  a = 9.8 v0 = 5 t = 5sec S=?

Q: 2) a) Find the unit vectors that are parallel to the tangent line to the curve y = 2sinx at the…

A:

Q: The region D bounded by y=0, x=y - 1, X x = as given in the following figure. YA 3.0+ 2.5- 2.0+ 1.5+…

A:

Q: Use a triple integral to find the volume of the region bounded by 5x + 6y, z = 7, and the planes x =…

A:

Q: 10. [VF² dx [Vr³ dx 11. 12. [Vx¹0 de 13. (u²+u+1) du 14. dv / ( ²0¹² + √² + v) du [w³+²+ w dw 15. w3…

A:

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A:

Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it dx dx d. S S…

A:

Q: d Using chain rule, what is the (2x-¹ + 3x)³ ? da O-24-36x²+54x*+81x 24-36x² +54x+81x8 24+108x²+54…

A:

Q: 5) A Cramer's Rule question: Suppose tickets to a football game are priced according to whether the…

A:

Q: Find the solution of the given initial value problem. ty' + 4y = t² − t +7, y(1) = 2, t>0 Y

A: We know that a differential equation of the form y'+P(t)·y=Q(t) has Integrating Factor (I.F.) =…

Q: Q.2// Find (A) f sin¹ (x) cos5(x) dx (B) f 4t³-t²+16 t t² +4 dt (C) Use improper integral to find ²…

A:

Q: (1,0), and (1,5). 5) Find the potential function of F(x, y, z) = (e² + ye*, e* + ze³,e³ + xe² ).

A:

Q: 4) A manufacturer has determined that the total cost C of operating a factory is C = 0.5x^2 + 15x +…

A: Given, total cost C of operating a factory is C = 0.5x^2 + 15x + 5000  where x is the number of…

Q: Given the function y = f(x) defined at all real values of x. Let x = 2, 3, 5 and 7 are critical…

A:

Q: dy M Find an expression for for the implicitly defined curve x2 - y³ = 0. Show all the steps in your…

A: As per the company's guidelines, we are supposed to solve the first three subparts for you, kindly…

Q: solution

A: Please refer to the image below

Q: fs = t³ - 1250t², when will the acceleration seconds)? O 5 seconds O 3.5 seconds O 4.5 seconds O4…

A: Using differentiation we get acceleration

Q: A ball is thrown downward with a speed of 13 ft/s from the top of a 169-foot-tall building. After t…

A: Basic quadratic equation and derivative are to be calculated

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A:

Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

A:

Q: f (x) = - 4x² - 6x x²+3

A: Given f(x)=4x2-6xx2+3To find the derivatives:

Q: What is the rectangular form of the parametric equations? z(t)=t-3, y(t) = 2t2-1, where t is on the…

A:

Q: SxVx² √x² - 4 dx

A:

Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

A:

Q: no working required just final ans

A: To solve the following problem

Q: Question 2 A. B. A system of linear equations is given below. 2x + y + 2z = 1 x + 4z = 2 y = 2z = 1…

A:

Q: integral

A: Please refer to the image below

Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: The line passing through the points 1,3,0 and 2,4,4

Q: d. dx √2√x+3+x e. S da x√4x + 1 f. dx x√4x²+1

A:

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

A:

Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2r. b) In the interval <x<³7, one normal…

A: Use equation of normal

Q: (: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw…

A: The given curve: x+y=1

Q: Simplify csc(t) sin(t) - cot(t) to a single trig function with no fractions.

A: csct-sintcott=1-sin2tsintcot(t)=costcottcott=cost

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a&gt;0 see below the answer and calculation

Q: Please check the numbers again. You have used 3/8 in the above equation. Euqation is 3/2.   I…

A: ∫sec2u du = tan(u)+C

Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx - (2xy + x²) dy…

A:

Q: Use integration by parts to evaluate the integral. 9x Saxe dx dx = S4x ex

A:

Q: e dx + (2y + xe") dy = 0

A: Given ey dx+2y+xey dy=0 Here M=ey and N=2y+xey ∂M∂y=ey  , ∂N∂x=ey Therefore,   ∂M∂y=∂N∂x is exact…

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

A: We have to find the interval in which f(x) and g(x) are decreasing.

Q: 4. Evaluate 12x+1 dx 5. Evaluate dx x 6. Evaluate 3x -¹ dx

A: Let's solve given integral.

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).