(a) Find the area of the region bounded below by the curve y = r² and above by the line y = 4 (b) This region is to be divided into two regions of equal areas by the horizontal line y = k. What values of k achieve this?

Q: 144-inch length of pipe is to be cut into 3 pieces. The second ece is twice as long as the first…

A: Topic:- geometry

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: Consider the following. 2x) dx (a) Find an approximation to the integral using a Riemann sum with…

A:

Q: rotational. essible.

A:

Q: 2. (x+2y-1)dx+(2x+4y–3)dy=0; when x = 2 and y = -1 %3D

A: We can solve the given differential equation by using the substitution . Substitute x +2y = v and…

Q: Find the verticies and foci, and sketch the graph: x2- 4y2 = 4

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

Q: Question Evaluate the following limit using L'Hospital's rule. lim + sin (6x) Provide your answer…

A:

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A:

Q: Find the solutions of the system of inequalities by graphing: x + y 2

A:

Q: Let f(x) = x In(1+x*). For all x E [-1, 1], it is known that (-1)" In(1+x) = -xn+1 %3D n+1 n=0 1.…

A:

Q: dy 2²+1 Use the quotient rule to find the derivative of the function y = dx О А. dy 1 = 2x(x+ V) –…

A:

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) 2…

A:

Q: Find the average value of f(x) = 4-x2 on the interval [2,3] Find the area enclosed by f(x) = -x2+4x…

A:

Q: Consider the following. y = x2 y = 20 − x   (a) Find the area of the region by integrating with…

A:

Q: 10. The vectorj^3E is the same as vector O j^4E O j^5E O j^2E O jE

A: Solve by vector product

Q: Performance Task A. Determine the antiderivatives of the following function. 1. S V4xdx 2. S(z +…

A: Please see the first three subparts below as directed by Bartleby.com.

Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

A: x=ρ sinφ cosθy=ρ sinφ sinθz=ρ cosφ

Q: Find the eccentricity, the type of conic, the directrix, and sketch a graph: r = (3) / (1 -…

A: Let's find.

Q: Let f be a continuous function. Show that 2022 f(1/a) dx f(x) dz. %3D 1/2022

A:

Q: Question 3 Find the domain of the folowing function 4xy fix.y)= O (kyly*x?} O {kylly2x) O (kylly>x)

A:

Q: 6. The definition of the first derivative is f(x+h)+f(x) E. f'(x) = F. f'(x) h f(x+h)-f(x) h…

A:

Q: #

A:

Q: Solve the following differential equations. 3. (cos 2x-x'y³+5x²)dx – (sin 2y+x³y²)dy=0

A:

Q: In the differential equation (x + 2y - 1)dx + (2x + 4y - 3)dy = 0 , we let the substitution w =…

A: Substitute w=x+2y

Q: x – 2 - Let g(x) x +3 (a) Find the third degree Maclaurin polynomial of g. (b) Approximate g(0.2)…

A:

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y2…

A:

Q: x 10°)(2.98 × 10-3) (2.446 x 10-3)(62.5) Express your answer using the correct number of significant…

A:

Q: _6. Which of the following is a particular solution to the differential equation when x= e5 and y =…

A:

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = Vx2 + y2, P(3,…

A:

Q: What is the value of e*dx? Select one: O a. 1 O b. 2 O c. The integral diverges. O d. e 8

A:

Q: 12vt dt (1+ t3/2)2

A: Given integral I=∫1412t( 1+t32 )2   dt

Q: In general, if f(x) is real and continuous in the interval from x to xy and f(x1) and f(xu). between…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Question Find the absolute maximum and absolute minimum of the function f(x) = = - 2r² + 4 over the…

A:

Q: please

A: We have to choose the correct option from the given options according to the given information

Q: Find a power series representation for f(x) = x2 1+ x3 ° By differentiating the power series…

A: To solve the following problem  Sncw it is not hiven as in where to find the exact solution at which…

Q: In how many ways can a group of 10 people be seated around a table if 3 of them insist on sitting…

A: We have to find number of  ways can a group of 10 people be seated around a table if 3 of them…

Q: Find the gradient of the function at the given point. g(x, y) = 13xeY/x, (5,0) Vg(5, 0) =

A:

Q: (7.84 x 10-8)

A: answer is in next step

Q: d the equation for the line that is parallel to the line with the equation -x + 2y = -9 passing…

A: Two parallel lines have the same slope.

Q: A box with a square base and open top must have a volume of 186624 cm³. We wish to find the…

A:

Q: The interesting relation is x^2+y^2 = 13. I have drawn it and completed part 1. Part 2 is determine.…

A: Topic:- geometry

Q: SOLVE the following DIFFERENTIAL EQUATIONS using appropriate method. FULL SOLUTION    (y^2 +…

A: To find the solution of the given differential equation.

Q: determine the relation x^2 + y^2 = 13. dy/dx in terms of x and y using implicit differentiation.

A:

Q: :-1 and g(x) = "- Vx +1 Let f(x)= arccos 2arctanx. (a) Find f'(x) and g'(x). V-1 *-2 arctan Vx ?…

A:

Q: 10 dr is The value of J5

A: The given integral,            ∫5101x2dx

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Given equation passing through the points (5 , -3, -2)  and  -23 , 23 ,1

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A:

Q: In(1+x) ferentiate f to determine the sum of the series n= +

A:

Q: {(-1)"n'e } ?

A:

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A: