Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y = //12 + Ce-x²/2 y = - =—=/27 + Cex ²2/12 12 dx 0y = - +/+ Cex ² 12

Q: for the following question above help me solve f

A: Given : for x<-1f'(x) = ddx(-x+1)=-1for x>-1f'(x)=ddx(-x2+3)=-2x

Q: Find the volume of the region bounded above by the surface z = 2 cos x cos y and below by the…

A:

Q: The revenue (in dollars) from the sale of x units of a certain product can be described by R(x)=…

A:

Q: Find y" by implicit differentiation. 2x³ + 5y³ = 2

A:

Q: A company operates two plants which manufacture the same item and whose total cost functions are…

A:

Q: Let f(x) f'(1) = = 4x²-3x+6 4x²+2x+8 Evaluate f'(x) at x = 1.

A:

Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

A:

Q: An explosion sends two shards of metal to the east and to the north. The northward shard travels at…

A:

Q: The elasticity of  x = f(p) = 1,875 - p2 when p = 10 is a can not be calculated b elastic c unit…

A: Given that, x = f(p) = 1,875 - p2

Q: Acme finds that its monthly revenue, in dollars, from the sale of x carry-on suitcases is 0.008x³…

A:

Q: Evaluate the integral. +C 3x + 0 x² - 4x + 20 da

A:

Q: 2. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x, y, z) :…

A: We have to use cylindrical coordinates in order to find the volume of thegiven region.

Q: Let f(x) = x³ – 5x² + 2x - 5. Find the open intervals on which f is concave up (down). Then…

A: The solution is shown below-

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. x³ + y³ = 6xy…

A: given equation is x3 + y3 = 6xy – 1   Rule: ddxxn=n·xn-1

Q: Find the derivate a) F(x) = 5-8x 1+ 2X f'(x)= 6) write all x-values (if any) at which the tangent…

A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

Q: Write out the form of the partial fraction decomposition of the function appearing in the integral:…

A:

Q: A spherical balloon is being inflated in such a way that the radius of the balloon is increasing at…

A:

Q: The region bounded by x=y and x = √y is rotated about the line y = -2. Which of the following would…

A:

Q: If a ball is given a push so that it has an initial velocity of 7 m/s down a certain inclined plane,…

A: We have to slove above question

Q: parallel to 2i - 6j+ k. x(t) y(t) = = z(t) = = of un throt lat is

A:

Q: Using the equation? = x^3/x^2 − 4 ? You need to show the following work -determination of x and y…

A:

Q: Find the future value of the following ordinary annuity. Payments are made and interest is…

A:

Q: Suppose you compute a derivative of a continuous function g and simplify it as the following: g'(x)…

A: A critical point of a function is defined as the value of x where the function or the derivative of…

Q: Determine which of the limits below are in a form where L'Hôpital's Rule applies. For those limits,…

A: The solution is shown below- As per bartleby guidelines only first part is allowed to solve. Kindly…

Q: Differentiate the function. g(t) = 4t-1/8 g'(t) =

A:

Q: Given f(x) = ln(3x2 + 8x + 2), find the equation of the line tangent to the graph of f at x = 0.

A:

Q: 1. Find the length of the arc of the curve y = 2²/23 (3x − 1) ³ from x = 0 to x = 7 33

A:

Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

A:

Q: For the following exercises, the vectors u and v are given. a. Find the vector projection w= proju v…

A: Given: u=5i+2jv=2i+3j

Q: Suppose f(x,y)=xy(1−10x−4y). f(x,y) has 4 critical points. List them in increasing lexographic…

A: We can solve the given problem by using the second derivative test.

Q: Determine the volume obtained by rotating the area enclosed by y = x(2 - x) and y 0 about the line x…

A:

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 20 m/s, its height…

A: We have to find the velocity.

Q: A volume is described as follows: 1. the base is the region bounded by x = -y² +12y +7 and x = y² −…

A: Given that x=-y2+12y+7 and x=y2-24y+151we have to find volume of object

Q: Find the slope of the line tangent to the graph of f(x) = 1/(2x−3) at the point x = 1 and please…

A:

Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

A: Given that:  3x + 5y = -2 and 5x + 3y = 2. And we find value of x and y ising gauss elimination…

Q: Find fo go h. f(x) X g(x) = x³, h(x) = x + 6

A: Given :

Q: Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the…

A:

Q: After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's…

A: Given that , fx=x6-2x , gx=x2+4x-59 , hx=2x-11 and mx=fx·gx , nx=gxhx

Q: If a ball is given a push so that it has an initial velocity of 6 m/s down a certain inclined plane,…

A:

Q: An investment company pays 8% compounded semiannually. You want to have $23,000 in the future.…

A: given future value of investment=23000 $ interest rate=8%=0.08 time= 5 year n=2 (because interest…

Q: (x)) = main of f(g(x)). (Enter your answer using interval notation.) (x)) main of g(f(x)). (Enter…

A:

Q: Use implicit differentiation to find y' for 4x³y² + ln(xy³) Answer exactly. y' (1, 1) = 4 and then…

A:

Q: Solve the following differential equation by finding h and k so that the substitutions x=u+h, y=v+ k…

A:

Q: 2. (a) ( 5) Evaluate مل ) + رند tim → o+ ** * → + x inx - Sin x

A:

Q: For the following graph, identify the points where the local and absolute maxima and minima occur.…

A: From the given graph we can conclude as

Q: Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and…

A:

Q: 7. Integrate the function 4ry³ over the region bounded by y = x, x=2, y = 0. (2.2) (0,0) (2,0)

A:

Q: Where does the line x = 5+1, y = 9-1, z = 21 intersect the cylinder x² + y² = 196? Enter your…

A:

Q: Consider the equation z*=x+y, where x,y and z are all functions of r. Which of the following is the…

A:

Q: Find the derivative of y = x²ª dy/dx =

A: