Create a bucket by rotating around the y axis the curve y = 2 ln(x - 2) from y = 0 to y = 4. If this bucket contains a liquid with density 860 kg/m³ filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s² for gravity. Work = Joules

Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: y = √√2x + 7

A:

Q: Which of the following is not true? 5 dx dx (A) lim S o 25-x² c+5-0 25-x² 3 dx dx So in (x²) B √₁…

A: We have to determine integration

Q: x6 cos(x³) (A) True (B) False |dx=0

A: We will solve the problem

Q: Can you write it in a paper? I don't understand

A:

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x - 4 and parallel to the line 6x…

A:

Q: Addition:Subtraction as___:antidifferentiation

A: We can answer the question as below.

Q: Find f^-1(x) for f(x) = 9+8x f^-1(x) = ____

A: Topic = Function

Q: (A) True B) False 3

A:

Q: Proving by Mathematical Induction A. 1. If P(2) = 1·3+2+4= 2(3) (11) 6 2. Prove that P(n) is true…

A:

Q: fx cos 2x dx

A: Let's solve given integration.

Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Find the length of the spiraling polar curve r = 6e50 From 0 to 2. The length is

A: SOLUTION-

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: We will find the solution.

Q: Find vertical asymptote, x intercept and y intercept of (x+1)(x-5)/(x-6)

A: Topic = Functions

Q: For the function y =f(x), it was found out that f"(c) = 0. What can be said that x=c? critical point…

A:

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

A:

Q: In evaluating S₂²² 2 dx 2 XV x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at given x.

Q: 2. Let S be the part of the cone z = √² + y² that lies between z = 1 and z = 3 with upward pointing…

A:

Q: Given the function y=f(x), y' is found to be positive over the interval (4,8), then over this…

A: if the first derivative of function is positive, then the function is increasing.

Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. HI-4 (a) lim f(x)g(x) #114 (b) lim…

A: Given problem:-

Q: Hewlett Plastics Inc. received a loan of $57,500.00 at 3.75% compounded quarterly to purchase…

A: We know formula for compounded interest:A=P1+rnntwhere A= Principal amount +total interest amount,…

Q: INTEGRO-DIFFERENTIAL 1. y" + 5y' - 4y = 0

A: Given: y''+5y'-4y=0 y(0)=2y'(0)=4

Q: Using Trapezoidal method √³x³dx for n = 6 is equal to Blank 1 (use 2 decimal places with proper…

A:

Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim x-0…

A:

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

A:

Q: 5. Given that W 8.25 √y The value of x,y and z are measured with maximum percentage error of 1%, 2%…

A: Let's find maximum percentage error in w.

Q: What monthly compounding nominal interest rate is earned on an investment that doubles in 10 years?…

A: We have to find the interest rate.

Q: Find the area bounded by y=-x²+1, y = − 2x + 2, x=-2, and y=2. (A) 5 B) 16/3 C) 1/3 (D) None of…

A: We can find the area as below.

Q: Using Simpson's method spaces) √²x² dx for n = 4 is equal to Blank 1 (use 2 decimal places with…

A:

Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: We have to find interest rate on the investment.

Q: Find the complete solution of e sinx-cos²x=0. dx

A: *Formula:- 1. ∫exdx =ex.2. sinxcosx = tanx.3.  1cosx = sec(x).4. ∫sec(x)tanx = sec(x).5. ey =x ⇒y =…

Q: Find the equation of the tangent lines and the normal lines to the curve y = √2x-1 at x=5

A: Find the equation of tangent line and normal line to the curve y=2x-1 at x = 5.

Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Given, f(x)=x24(1-x)

Q: Find the derivative of sin In x O sin(Inx)/x O cos(Inx)/x O cos(1/x) O sin (1/x)

A:

Q: A bank has decided to set its interest rates to compound monthly on all deposits in order to give…

A: We know the compound interest formula:A=P1+rnntwhere A=Principal amount +interest Amount…

Q: Solve the differential equation: (1+x3)dy - x2ydx=0; y(1)=2

A: Solve the differential equation: (1+x3)dy - x2ydx=0; y(1)=2

Q: 0,000? e marginal revenue is dollars per item. necessary, round to the nearest integer

A:

Q: Use the one-to-one property of logarithms to find an exact solution for   ln(2)+ln(2x2−6)=ln(69)…

A:

Q: B.) For numbers 1 to 10: Determine if limit of each function exist using the piece-wise function…

A:

Q: b iff and g are continuous on [a,b] and f(x) z g(x) for all x E[a,b], then f(x) dxz g

A: SOLUTION-

Q: Cynthia's investment of $81,200.00 in a fund matured to $160,353.29 in 7 years. If the interest in…

A: We want to calculate period and nominal interest rate.

Q: Q2: Find Maclaurin series for the function f(x) = (4-x) (four terms only), then find the error…

A:

Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.7q+950, what profit can be…

A: We need to find profit.

Q: x² +2 (x-2)(x² - 2x+2) dx S U 2-2x 3 (√(√72²2²2²X + 2 + x ³₂ ) dx

A: ∫ x2+2x-2x2-2x+2dx

Q: Question 1 Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then [f(x)dxz g(x)dx…

A:

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: Which of the following is not true? A √ in(x²) dx = lim_ sin(x²) dx 3 3 dx dx Ⓒ 1² B In(x²) - = lim…

A: Solution is done in step 2