24 How many 3 letter codes can be formed from the word PROJECT if letters cannot be repeated? 7C3 7! 7P3 73

Q: 1) Find the derivatives of the following. Simplify your final answers. a) f(x) = 2 2x T sin 2x + 2x…

A: a) f(x)=[2x1/2-3x2/3/2]/(1-x) -pi sin2x+(e2x+2x) 1/2-lne. Repost the next parts.

Q: Use the Laplace transform to solve the following initial value problem: y" + 4y/ + 29y = d(t – 5)…

A: Taking Laplace transform on both sides and solve it.

Q: Find the derivative of the function y = xta{z) y =

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Q: Let f(x) = 3,/a If g(x) is the graph of f(x) shifted down 1 units and left 3 units, write a formula…

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Q: Calculate the Taylor polynomials T2 and T3 centered at a = 0 for the function f(x) = 11 tan(x). %3D…

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Q: Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=5.

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Q: 5. Jimbo runs a lemonade stand where he sells 150 cups of lemonade a day, charging $8.00 a cup. His…

A: To calculate the Price function and the marginal revenue.

Q: c) L{S,T sin t dt

A: Given,          ℒ∫0tςsinςdς

Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: Number Problem The sum of two numbers is twice their difference. The larger number is 6 more than…

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Q: Use linear approximation, i.e. the tangent line, to approximate √81.1 as follows: Let f(x)=√x. Find…

A: Explanation of the answer is as follows

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2, 15) - (-) 3 v = O parallel O…

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Q: 18. A farmer wants to fence in a rectangular plot of land adja- cent to the north wall of his barn.…

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Q: dy Find dx using implicit differentiation. 5x = 2y° +7y dy dx

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Q: Prove by contrapositive. if x and y are integers such that x > 1, and x divides y, then x / (y +1)

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Q: Find the equation of the tangent line at the given point on the curve. 2x2 + 2y? 29y-y e 58x/5, .2…

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Q: Directions: Solve the following problems completely. Mark your final answer. A. Find the equation of…

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Q: Find the interval of convergence of E(-1)". n 2n 36" n=0

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 %3D y + 5 =…

A: The given question has been solved in detail.

Q: Using the graph find:  f'(2) g'(2) d/dx [5f(x)+3g(x)] | x=2

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Q: Find the derivative of the function (2y – 1)3 Vyt +1 G(y) = In G' (y)

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: Given query is to find the integral.

Q: A spherical snowball is melting.  It's radius is decreasing at 0.2 cm per hour when the radius is 14…

A: A spherical snowball is melting.  It's radius is decreasing at 0.2 cm per hour when the radius is 14…

Q: ind the definite integcal uoing any method. 3/2 x13-2xdx

A: Follow next step

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic…

A: As we know that the nth order Taylor's polynomial at x=0 is given by,…

Q: Determine the exact interval(s) over which the function y=x(ln x)^2 is: A) Increasing and…

A: We have to find monotone intervals and concavity.

Q: Use implicit differentiation to find y′ and then evaluate y′ at ​(−3​,3​).   4xy+y+33=0       Part 1…

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Q: egion bounded by f(x) = Vx, y = 0, and x = 4 is shown below. nd the volume of the solid formed by…

A: Given query is to find the volume of the solid generated.

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: Evaluat each Integral. For definite integrals, give exact valaes Only, rF - 7+" -ム dt

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Q: Graph the function and its inverse using a graphing calculator. Use an inverse graphing feature, if…

A: To solve the following problem

Q: Can

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Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)=sin x- cos x- tan x tan x D.…

A: Follow next step

Q: 4 d) En=2n-1 4n2 e) 0 En=1 n2+1 4 f) En=2 n2-n (Use partial fraction decomposition)

A: Explanation of the answer is as follows

Q: The count in a bacteria culture was 500 after 20 minutes and 1100 after 40 minutes. Assuming the…

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Q: Researchers have found a correlation between respiratory rate and body mass in the first three years…

A: Here, the given function is: log R(w)=1.85-0.48log (w)...(1)

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: A region bounded by f(x) = - x + 5, y = 1, x = 0, and x = 5 is shown below. Find the volume of the…

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Q: with the limit definition of a derivative find the derivative of g(x) = (x-1)^2 + 1

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Q: a) L{te-3t cos 3t}

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Q: Determine whether the following equation represents an exponential growth or exponential decay.…

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Q: Find the dimensions of the rectangle with maximum area that can be in- bed in the ellipse x²/a² + y²…

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Q: 2x find fz" a x dx

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Q: 29. What is the lim f(x)? 2 В. DNE С. -2 D. -4 A. O A O D 30. At which value of x is the graph…

A: Solved below

Q: 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -5 -64 The graph above is a transformation of the function x…

A: Topic:- function

Q: Consider f(x,y) =x'+y* +2ry-x+5. Find its critical points and use the second partials test to…

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Q: If m s f(x) < M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

A: Given problem:-

Q: Given that f(m) = a"h(x) h(- 1) = 4 h'(-1) = 7 Calculate f'(- 1).

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Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. 5 dx sec x-1…

A: Here we have to evaluate the given integral.

Q: n-1 £(- Given the series 8 n=1 Does this series converge or diverge? O diverges converges 6 If the…

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