Define R as the region bounded by the graphs of f(x) = 6x - 5x² and the x-axis. Which of the following represents the volume of the solid of revolution formed by rotating R about the y-axis?

Q: v − 1) dx + (x + 1) dv=0. If v= 2 when x = 1 determine v when x =

A: The given differential equation is; x(y+1)dx+(x+1)dy=0

Q: 26. The graph of y = f '(x) is shown below. List the intervals where the graph of f is concave up. O…

A:

Q: b. Z Z-3

A:

Q: Need this in complete and handwritten solution, thank you! Find the Differential Equation of the…

A: We have to find the differential equation of the Family of Ellipses with its center at the origin.

Q: 1. Where does the graph of s= t² - 3t+2 have horizontal tangent? Write an equation for the tangent…

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: Evaluate the integral|5x-1| dr. Answer:

A:

Q: Eliminate the arbitrary constant. 2x -X y=c₁e + c e 1 2 A B с D y" y'- 2x=0 y"-y'- 2y=0 2y"-y-2x=0…

A:

Q: 2. y' ysecx

A:

Q: Write the interval of continuity for the function below: sin(x)√81-x2 x²+x-6 f(x) -

A:

Q: Find the domain and range of: 1) y = 2) y =√1-x², 3) y = x² - 2

A: We can find the domain and ranges in the below steps.

Q: A There is no correct answer from among the given choices. differential equation by separation of…

A:

Q: f In dx

A:

Q: Find a,b to continue the function at x=3 if: ax + b f(x): = 2ab + 1 bxa + 3 x > 3) x = 3 x < 3)

A:

Q: Evaluate the limits given the following information: lim f(x) = 6 lim g(x) = -9 24-6 x--6 a) lim x 6…

A:

Q: B. by factoring 1. x² + 7x = 0 2. m² + 8m = -16 3. x2 + 5x − 14 = 0 4. 2y2 +8y - 10=0

A: Topic = Quadratic equation As per guidelines , At a time only three sub-parts can be answered.…

Q: Closed book, closed notes, no calculators. You have to show complete work for full credit; make sure…

A:

Q: ****** 0 Find the value. (Enter your answer in radians.) As x→ -1, the value of arcsin x → EN 2

A:

Q: Given f(x) = 5x² - 10x + 8, find the average rate of change of f(x) on the interval [2, 2+ h]. Your…

A:

Q: Q4: Solve the following integrals:- dx ³-2x² (1) dx (2) √ √2√9-1² (3) fx² sinxdx (cos-14x)² 1-16x²…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Given that f(x) and g(x) are continuous functions, and g(4) = lim (2ƒ(x) + f(x)g(x)) = − 4 x 4 ƒ(4)…

A:

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 lim 5 4 3 x→2 12 A -1 -2 -3 -4 -5+ Select all…

A:

Q: Find dy/dx for the following functions:- (2) y = v sinh Vtan x (4) y=2,u = 3x²-2 u²+1

A:

Q: Let h(x) = f(x) + g(x). If f(x) = 2x² and g(x) = 8x5, what is h'(x)? Do not include "h' (x) =" in…

A:

Q: fcos (x) sin(x) dx

A: We need to find out the integration of the given integrand.

Q: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

A: Here is the solution:

Q: Relative change is the ratio of the amount of change to the original amount. In this case, this…

A: To find out the relative change in the average household income from 2008 to 2018.

Q: Solve the differential equation 4. xdx e-x + (Y+) dy y³

A:

Q: 1. f(x) = sx (x+1 if x ≤ 0 if x > 0

A:

Q: Let u(t)=9t³i + (t²-1)j- 4k. Compute the derivative of the following function. u (tª - 2t) Select…

A: Apply the derivative for the function as given in the question.

Q: x²y = 1 + cx

A:

Q: 3. Check that each given function is the solution to the initial value problem. y(0) = 1, y'(0) = 2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: (2) S dx x²√9-x²

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

Q: For the homogeneous equation (y² + 2xy) dx -x²dy = 0, which is a better substitute: letx=vyory=vx?…

A: The given equation is; (y2+2xy)dx -x2dy=0.

Q: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

A:

Q: A V(t) = -1,700t + 32,000; value after 5 years = $23,500

A:

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: Solve (xy + 4a²y)dy = √(xy-5a³ + ax - 5a²y)dx

A:

Q: Question 2 Nontando kept water bottles in a rectangular box with ice cubes in order to sell them to…

A: To find out the diameter of the water bottle in millimetres.

Q: Solve the initial value problem. 1 dy y cos 0 0 de 2 y +1 , y(x) = 1

A:

Q: Solve for the variable of the following quadratic equations. Kindly provide a COMPLETE and CLEAR…

A: We have to solve the given quadratic equations.

Q: 30. dy dt t y-12y y(0) = 4

A:

Q: Q6) (E.G.) If AABC~ A EFG, 2A 3EG and the perimeter of AABC is 12. Then the perimeter of A EFG is:…

A:

Q: If A = 1=1 ²₁₂ 21₁B =[ ²¹/₂ 3 b) B.A c) A-2B a) 3A-C 3] -2 = [3²5] 4J and C= Find:

A:

Q: Eliminate C from the equation y=3x²+ Ce=2x. Ay'-2y-6x²+6x=0 B) y'- 2y + 6x² - 6x=0 Ⓒ2y+y'+3x²+6x=0…

A:

Q: What is the summation form of the Maclaurin series for 1/(sqrt(1-x2))? Hint: Find the first few…

A: Solution:

Q: Solve the Differential Equation x² (y² +3) y(x³+1) dy + dx = 0

A:

Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: t10 x csc x dx 6 cot 10

A:

Q: Write the interval of continuity for the function below: tan(sin(x)) log3 (7) f(x)= = for 0 < 2T

A:

Q: The point P(1, 0) lies on the curve y = sin( (a) If Q is the point (x, sin(¹3″ )), find the slope of…

A: