The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in figure below. Use the shell method to find the volume of the solid generated by revolving the region R about the y-axis. y = x² – 2r + 2 5 4 3 2 6

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

A:

Q: Differentiate the following functions. Show your complete solutions and emphasize your final answer.…

A: 1) f(x)=25x    Differentiate with respect to x   f'(x)=252) f(x)=-4x5+2    Differentiate with…

Q: e-2 1 Evaluate: e-3 xInx Oc -In 6 O d. In 6 2/3

A:

Q: u+v+w=0ad u =3, v=5, w = 7 then he angle between y and y is 0 2r 6. 0 5m ONone of the choices 11

A:

Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Q2) Convert the polar function r = tan20 to cartesian. %3D

A: Let's find.

Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Q3) Evaluate triple integral dz dy dx.

A: A detailed solution is given below

Q: Find the saddle pointis of the function f(x,y) = x° +y°+i y+4 Oa(5-1) Oc (4.0) & (4,0) Od(0.0)

A:

Q: For the functionf(x) given below, where x > 0, evaluate lim f(x). X00 f(x) = In(3x' – 3) – In(4x² +…

A:

Q: csc ² 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. A True B)…

A:

Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

A:

Q: Find the absolute extrema of the function on the closed interval. (x) = 7x2 + 1, (-1, 2] minimum (х,…

A:

Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: -6x-'dx

A:

Q: Evaluate fs 2°ds O a. 2*(sln2 - 1) (In2)2 O b. 2(słn2 - 1) (In2)2 O C. 25 - 1) In2 O d. 2° (+ 1) +1)…

A:

Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

A:

Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x² + 16

A: To evaluate: I=∫dx9x2+16 Substitute x=4sec u3⇒dx=43sec u tan u du

Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

A:

Q: x- 2 For the function f(x) = x-5 a. the graph of the function is until x = 2 only. O b. the graph of…

A:

Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: Suppose A = (a, 0, 2) and B= (6, –2, b), for some a > 0 and b> 0. (a) If projĄB = 12 24 =,0,), find…

A: Suppose A=a, 0, 2 and B=6, -2, b, for some a>0 and b>0.If projAB=125, 0, 245, then to find the…

Q: Let a = 2i - 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8

A:

Q: A. Evaluate the limit of a function using the concept of Special Limits. 1. lim t→0 t t2-3t+5 + t2-1…

A:

Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x² + 16

A:

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

A:

Q: dy Vy+2 sinnx costx dx

A:

Q: Find the general solution of (2x – y) dy = 2y – x - da

A:

Q: Find the AuRtaYe value of f(x) = x* on the intervai 2,67

A: answer is in next step

Q: Use the first principles definition of the derivative to find f"(2) where Ax) = O a) 0.125 b) 4 c)…

A:

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of, does the curve has…

A: Given

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = for f(x) = cos(x). %3D T2(x) must…

A:

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: Question 1 Which of the following is the Taylor series expansion of the function 'f (x) =e¬x² with…

A: Given problem:-

Q: Helene invests Php 5,000 in an investment that earns 6% per annum. How many complete years doe it…

A: Topic = Algebra

Q: Question 5 For what value of a is the function t-1, - 10<t<3 f (x) = t²+ 10t, 3<t<10 continuous? O…

A:

Q: Find (a) if fx) = /x-a+1.

A:

Q: Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 +…

A:

Q: Let r(t) = (t', 1- t, 4t). Calculate the derivative of r(t) - a(t) at t= 4, assuming that a(4) = (9,…

A:

Q: Find the total distance traveled by a body and the body's displacement for a body whose velocity is…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A:

Q: Find the volume trapped between the cone z = 2 – Vx² + y² (upper) and the paraboloid z = x² +y².…

A: We need to find volume.

Q: Q4) Find plane area inside the polar function r = 2sin E-0) and outside T= sin in-e) in first…

A:

Q: 12x 3 3 15 12 x4

A:

Q: For item # 6, use the product rule. 6.) f (x) = (x³ – 1)(4x + 5) %3D | x+3 7.) f (x) = 5х-2

A: Here we have to differentiate the given functions.

Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydr (8r+7)dudy O none of the oices

A:

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

A:

Q: Solve the D.E dy – (2x/1- y2)dx = 0

A: