The area between the curve y=x2, the y-axis and the lines y=0 and y=2 is rotated about the y-axis. Find the volume of the solid of revolution formed.

Q: Evaluate lim x-0 1-√√1+x X

A: Given problem:-

Q: (CLO-3) Find the area between the curves y=12-x2 and y=x²-6-

A: We have to find the area between the curves.

Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: Evaluate the integral. π/2 sin³ 0 cos²0 de 3

A:

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (1,1)

A: To find the linearization Lx, y of the given function at each point.fx, y=x2+y2+1 a 4, 1b 1, 1

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e6xy = sin…

A:

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A:

Q: Evaluate (ƒ¯¹) '(2) for the function 3 2 f(x) = √√√x³ + x² + x + 1. Explain your reasoning and write…

A: The given function is  f(x)=x3+x2+x+1

Q: [CLO-2] Find the derivative of f (x) = x −x5 e 2x + 3 1-5x4 x-x5 x-5x5 2/x −x5 1-5x4 Vx-x5 −5x4…

A:

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

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

Q: 3 Só ( x + ²/2 ) ²³ dx X

A: integration

Q: 4. Calculate the average value of each function over the given interval. Hint: use the identity sec²…

A: Average is evaluated.

Q: Find at least 5 distinct rational points on the unit circle in the first quadrant of the plane.

A:

Q: This question is designed to be answered without a calculator. Use this graph of function f. y 5+ in…

A: Here, from the given graph the function is continuous at x=0,2,4 but not continuous at x=-2 because…

Q: Find the Inverse Laplace of a) (3s-8)/(4s2+25) b) 2/3s+9 c) 5s+4/s3

A:

Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 using Lagrange…

A: answer is in next step

Q: Two capacitors with capacitance of 6 μF and 4 μF are connected in series across a 100 V dc source.…

A: Question- Two capacitors with capacitance of 6 μF and   4 μF are connected in series across a 100 V…

Q: Given the following functions: ind: f(i(x)) f(x) = 3x² − 5x + 2 g(x) = 7x² + 3x - 1 2x - 7 h(x) = 5x…

A: Given query is to find indicated composite function.

Q: Given the polar coordinates (1,7π/8) determine (x,y). What is x=______. (round to 3 decimal)

A: In this question, we need to find the rectangular coordinates (x, y) from the given polar…

Q: What do you call the numbers below. Ta(1) 2= 1^3 + 1^3 Ta(2) = 1729 = 1^3 + 12^3 =

A:

Q: Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

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

Q: 8. 9. 10.¹₁²(x² (2-y)dy dx π/4 /²x cos y dz dx dy + y² + z²) dx dz dy

A:

Q: Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y =…

A: Let's find definite integral of arc of length of given parabola y =4-x^2.

Q: tan2x-2sinx lim x→0 x3 a. 0 b. infinity c. 3 d. DNE Find the slope of the curve y = 64( 4 + x) 1/2…

A:

Q: Calculate the Taylor polynomials T₂(x) and T3(x) centered at x = a for f(x) = 18 sin(x), a = = 1/2.…

A:

Q: (e²t-e-2¹) ² None of the choices Option 1 1 S 32 s(s² - 16) I Option 3 + 25 1 s+4 32 s(s² + 16)…

A:

Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: 2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

A:

Q: Given R(t) = 4 costi + (1+ 3cost)j +5sintk. Find N(t) at t = = www. N(t) = ----k 10 Option 1 N(t) =…

A:

Q: 1. If F(x) = Le d ex dt, find F(1) and F'(x).

A:

Q: Find the derivative of the function at Po in the direction of u. g(x,y)= x-y 3xy + 2' Po(-1,1), u…

A:

Q: (c) 1 e¹/x x² dx

A:

Q: lo 3 Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar…

A: Let's change given Cartesian integral to polar integral and then evaluate.

Q: Find the particular solution (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1 What is the particular…

A:

Q: 3 Find x=x-12 lim. x-7-3 x2+ 8x+15)

A:

Q: Find the general equation of the conic with the given properties. 51 59 1. A parabola with directrix…

A: Given: A parabola with directrix y=-5132 and one endpoint of the latus rectum at -18, -5932

Q: This question is designed to be answered without a What is the particular solution of d = 2xy-y…

A: Solving the differential equation by seperation of variables.

Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

A:

Q: S52² +32° +22²-32 +2) dz

A: Solving the problem by finding the value of integration.

Q: Solve the following differential equation on the interval (0, ∞) (in other words, dy y² = x² + y² dx…

A: Solution of given question is written in below steps.

Q: A retailer has been selling 1,000 computers a week at $750 each. The marketing department predicts…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4.3√√√7

A:

Q: Find the general solution of nx dx = (x + 1)² ylnx

A:

Q: How many combinations can be made from ♣, ♠, ♦, and ♥ if taken a) four at a time? b) three at a…

A: solution:-♣, ♠, ♦, and ♥  are four different itemswe know that  combination is the selection of…

Q: 2/ Find the equation of the tangent line at (0,0) to fex) = xex хе 2 -X

A: Given f(x)=xe-x2y=xe-x2Differentiate…

Q: In(x²y)- ez-tan"¹ z. Assuming that z is a differentiable function of x and y. Let F(x,y,z) Find F.…

A:

Q: Evaluate the following integrals: O •(Cartesian to Polar) Civen the cartesian coordinate find FOUR…

A: Follow the procedure given below.

Q: If f(x) = f*^²}} 2-1 5 1+1² dr. then what is f'(-3)?

A:

Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

A:

Q: x = 2t² and y = t³ - 3t has a point where there are two tangents. Identify that point.

A: