Looking for some advice on this problem please! By using derivative, determine the intervals of x where the function increases and decreases: y = 3x^5 − 5x^3 +9 Find the coordinates (x, y) of the points of local maximum or minimum and, for each point, explain why it is a local maximum or minimum.

Q: Find the volume of the given solid region bounded below by the cone z= sqrt(x^2+y^2) and sphere…

A: Here we have to find the volume of the solid region.

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(8y) dy =…

A: Let's solve given diffrential equation.

Q: - show that V(x,y) = x 'f (2x+y)

A:

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A:

Q: For items 22-23: The equation of a curve is y = 6tanx. 22. What is the slope of the tangent line…

A:

Q: The derivative of f(x) with respect to x is the function f'(x) and defined as f(x+h)-f(z) f' (z) =…

A: topic- derivative of a function

Q: 7. 1 x lnx dx 8. f(x + 1)(2x - 1) dx

A: 7.∫1x lnxdx = ∫1 lnx. 1xdxLet, lnx= y ⇒1xdx = dySubstitute the corresponding values in the…

Q: Problem. Compute the general solution of the following 3 x 3 linear system: -2 3 dY 3-2 1 Y, where Y…

A:

Q: x²-5y²-3x-y +22=0 (y-2)(x-y-2) = 0

A:

Q: A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as…

A: Trigonometric ratio

Q: ¹In(1+x) -dx 0 X

A: Expand log series

Q: What is the derivative of y = √5x² + 3x + 2 where x = 1? O no correct answer O2.054 O 2.057 O2.056 O…

A:

Q: e dx + (2y + xe") dy = 0

A: Given ey dx+2y+xey dy=0 Here M=ey and N=2y+xey ∂M∂y=ey  , ∂N∂x=ey Therefore,   ∂M∂y=∂N∂x is exact…

Q: The fox population in a certain region has a continuous growth rate of 4 percent per year. It is…

A:

Q: Find the direction angle of v for the following vector. v=3i-8j What is the direction angle of v?

A:

Q: > Write a triple integral including limits of integration that gives the volume of the cap of the…

A:

Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

A:

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A:

Q: Find the eigenvalues of A³ for Enter the eigenvalues in increasing order. Eigenvalues of A³ are: i i…

A: Cayley Hamilton theorem and basic property of eigenvalues are used

Q: A lighthouse is on an island 300 meters off shore. The lighthouse beam makes a full turn every 7…

A: Let's solve.

Q: hand written plz 1 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = (a)…

A:

Q: Evaluate y' y = cosh²12x +sinh²6x

A: To find out the derivative.

Q: Let V₁, V₂. and v3 be vectors in a vector space V, and let T:V→→ R³ be a linear transformation for…

A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural…

A: a) As a is a real number, then it can be written as sum of a natural number and a fraction.  Hence,…

Q: Kindly answer the question and provide a clear and correct solution. If I still get wrong…

A:

Q: SET-UP a triple integral that will solve for the volume inside the sphere x² + y² + z² = 2z and…

A:

Q: 3. Output, P, is produced using two inputs, K and L, according to P= f(K, L) = 2 + KL-2 5 1) Find…

A:

Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

A:

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: SOLUTION-

Q: Find the derivative of f (y) = 5 sin6 (yª).

A:

Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

A:

Q: 10. [VF² dx [Vr³ dx 11. 12. [Vx¹0 de 13. (u²+u+1) du 14. dv / ( ²0¹² + √² + v) du [w³+²+ w dw 15. w3…

A:

Q: Question Define R as the region bounded by the functions f(x) = 2x + 1 and g(x) = x + 1 between x =…

A: The functions f(x)=2x+1 and gx=x+1 between x=1 and x=3, the region is revolved about x-axis.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. - eu du (6 - e4)²

A: topic- indefinite integral

Q: Svi-x2 1-x2 dx

A: We will solve the problem

Q: [Select] derivative of y? y = = x²e²x+1 18. Which rule is applicable when solving for the A.…

A:

Q: For each of the following, find (i) the direction of P₁P2 and (ii) the midpoint of line segment P₁…

A: Given, P1(1,4,5)P2(4,-2,7) Therefore position vector of P1 and P2 is p1=i+4j+5kp2=4i-2j+7k

Q: Team Alpha was on their night patrol in Mystical Forest when they suddenly noticed that a flare was…

A: here distance we have to find  a = 9.8 v0 = 5 t = 5sec S=?

Q: x² +11x+30 4x+20 For items 37-38: Given the function f(x) = [Select] 37. What is f' (6)? [Select]…

A: Given  f(x) = x2 +11x+304x +20    ------(1)

Q: 27. Given f(x)= F(D)=2 (X+) (x-1) A. I only B. II only x² -1 2 6 x #1 x = 1 I. II. III. e shituse…

A:

Q: What is the derivative of y = sinx x³ ?

A: Given that,   y=sin xx3

Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

A:

Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, t€ (-∞0, +∞0).…

A:

Q: A certain drug is being administered intravenously to a hospital patient. of the drug enters the…

A:

Q: Find the derivative of f (x) = (x8 – 5x) (x² f(x)= + 10x 10).

A: Topic = Derivative

Q: Region R is a plane region bounded by the curve y = 32, the y-axis and the lines y = 1 and x = 4.…

A: We have to find the area and volume.   According to our guidelines we can solve only three subparts…

Q: As shown in the required readings or videos find the general solution to the differential equation…

A: Here we have to find the general solution of the given differential equation,  y'+2y=2ex…

Q: Consider the function f(x)= = x² + 7x + 12 -2 a. Find the first derivative. f'(x) = b. List any…

A:

Q: Given cost and price (demand) functions and C(q) = 115q + 31000 and p(q) = -2.3q +800, what price…

A: Marginal Profit=Marginal Revenue-Marginal Cost