Three pens of the same size are to be built along an existing fence. If 480 feet of fencing is available, what length should x and y be to produce the maximum X total area? What is the maximum area? feet

Q: Find the Area of the hegion baudded by the ghaphs Of y=x3 and Y = 4x Using integtation Determine the…

A: Given:      y = x3       y = 4x

Q: S sec°x tan x dx +C + C sec³x + C

A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

Q: Q3 Find y ン ニ月(^)→ t(メッ) tanx 2 y-(1+x)

A:

Q: Find the inte gral. Box Final Answer. For the definite integral, give the excact answer only dx

A: Answer is in below steps.

Q: Question 8 x2 + 64 Using trigonometric substitution, given - dx, the simplified form of the integral…

A:

Q: Set up, but do not evaluate, an integral for the surface area of the surface generated when the…

A: writing given function as x in terms of y

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: Su Find D. andR X -1 %3D Xマ→!

A: Explanation of the answer is as follows

Q: A particular solution of the differential equation y+4y =8sin2x is Select the correct answer. O a.yp…

A:

Q: Find the general solution of the differential equation. у" - 400у %3D0 ... y(x) =

A:

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A:

Q: 1. A business wants to manufacture a huge closed box with a square base a square top and rectangular…

A:

Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

A: Solving

Q: (a) Consider the following. -5 5 5 -5 Identify the surface graphed. O cylinder O paraboloid O cone…

A:

Q: Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx…

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 2et…

A:

Q: Given t = x + ex, find dx/dt

A:

Q: Use implicit differentiation to find dy/dx. 13) 2хy - у2 - 1 A) _ у -х B) X - y C)L X - y D) – y - x

A:

Q: 11) у - еx4 In x ex4 + 4x4 ex4 In x A). + 4exª In x B) 4x4 ex4 + 1 C) D erg + 4x3 ex4 In x

A:

Q: csc*n y 7. S dy cot²n y

A:

Q: S xdx can be solved by either algebraic subsitution or integrataion by parts. Vx- 1 A True B False

A:

Q: Question 1 Which of the following are subspaces of R ? Choose all correct answers. {(x, y, z) E R³ |…

A: Only option 1 and 3 are subspace of R^3

Q: Determine the general cquation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

A: We have to find equation of ohm plane

Q: Find the absolute extrema of the function on the closed interval. f(x) = 6x + 1, [-1, 2] minimum (x,…

A: Finding extrema of a function. We can find the extrema of a function of function f(x) by  finding…

Q: 1 Y(s) : s2 + 7s + 10 a. y(t) =(e-5t – e24) b. y(t) =(e-5t + e²') c. y(t) =(e5t - e-2t) d. y(t)…

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Q: In XVX2-625 dx , if we let x-25sece, then dx = 25secede. A True B) False

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Q: Prove the product rule of differentiation.  That is prove that if p(x)= f(x) g(x), where  f(x) and…

A:

Q: Decide whether the limit exists. If it exists, find its value. fx) 3+ 2+ -2 -1 3 X -1+ -2- 1) lim…

A:

Q: и + Use the ratio test to determine whether > converges or diverges. п! n=12 (a) Find the ratio of…

A: Here, the given series is: ∑n=12∞n+5n! Let, an=n+5n!; n≥12

Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j+…

A:

Q: Q38: If y = e2x sin 5x, then which of the following is true? (a) y" – 4y' + 30y = 0 (b) y" – 4y' +…

A: Given,            y=e2xsin5x

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given problem:- Find an equation of the plane with the given characteristics. The plane passes…

Q: In each of the problems, solve the given differential equation. 1. y` = 1 + x + y2 + xy2 2. y` =…

A:

Q: y" + 4y" + 4y' = 0. %3D

A: Follow the procedure given below.

Q: 100 10) y = 2 + 9e-3x

A:

Q: Find the volume of the solid obtained by rotating the region underneath the graph of the function…

A:

Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: x² – 25 S The antiderivative of dx is V x2 – 25 – sec-lx+ C. A True В False

A: follow next step

Q: dx = x +C 3. 45x dx = -5x +C 4. 12V dx =-x+2x' +C 4x + 35x 4. 4 +8x dx = -5xi +C 4 28x 15x dx = 4x+-…

A: The integration of the integral  35x3/4/4 +8x-3.

Q: Use the following information to complete parts a. and b. below. f(x) = - a = 3 a. Find the first…

A:

Q: Consider the following piecewise function Quiz Content x² – 1 x 1 x2 Find the value(s) of a for…

A: Use the definition of  continuous function .

Q: Evaluate the definite integral. NOTE: Enter the ecact answer. 13 ti+t°j dt

A:

Q: Reduction of order can be used with y = 3x to find a second solution for the DE: xy" + 2xy' + 2y =…

A:

Q: Find dy dx I-Ln(x+3)=tかが(x:)

A:

Q: Which of the following evaluates the double integral xy dA,

A: We can solve this as follows:

Q: -is F (x) xỉ (9x“ – 10) where "a" is equal to The antiderivative of f (x): 30 A 12 6. 1 D None of…

A:

Q: nd derivative of f(x) = x In(x)

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

Q: 25 – x² In -dx , if we let u=/25- x2 , then udu= – xdx. T True F False

A: Follow next step

Q: Let A = (1, -2) and B = (6, 2). Solve for projyA. %3D

A: projBA  implies projection of A on the vector B. projBA =A·BB2 B  ............(1) A·B is dot product…