Integral of (5x3 + 1 - x4) dx

Q: 2. Evaluate dy and Ay for f(x) = 30 + 12 x²-x³ at at x = 2, and dx = Ax = 0.1

A: f(x)=30+12x2-x3dy=f'(x)dx∆y=f(x+∆x)-f(x)d dx(xn)=nxn-1d dx(constant)=0

Q: Find the tangent plane to the equation z = 4y cos(5x – 3y) at the point (3,5,20) z =

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Q: sequence of 10 letters from 10 A 10 8 10 C A code a) How many? (b) Even number of A and odd number…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

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Q: Help me differentiate and simplify 1a-1d

A: Here we have to find the derivative.

Q: For the equation given below, evaluate dy dx at (1, ²) = dy dx at the point (1,1). Y x - 6y = x³ - 3

A: yx-9y=x3-3(1,211)d dx(xn)=nxn-1

Q: Ana and Beverly, produce the same product on identical machines. Ana receives $25 per hour and…

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Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded by the…

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Q: Calculate the derivative of the following function. 5x y= 2x+7

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

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Q: Hugo is serving fruit sorbet at his party. He has 1 gallon of fruit sorbet to serve to 32 friends.…

A: total fruit ara 1 gallon total peoples are 32we know  1 gallon=16 cups

Q: 8. Determine the dot product of u = [5,-3,1] and v = [2.–2,

A: The vectors are given as u→=[5,-3,1]v→=[2,-2,3].

Q: Let f'(x) = f(x)= x cos ³

A: The given function fx=xcosx3. We have to find its derivative.

Q: Find three numbers whose sum is 24 and whose sum of squares is a minimum.

A: Let three numbers are x,y,z

Q: the given second-order differential 1. 2y" - 72y = 0

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Q: 3x 2. Determine the derivative of f(x) = (1 using the product rule and chain rule (cannot use…

A: Given : for x = 0 y = 0 derivative of function

Q: For the equation given below, evaluate y' at the point (-2,2). e +24-e² = 4x² + 2y². y' at (-2,2)=

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Q: Given that lim f(x) = 9 X→ 1 lim h(x) = 0, X→ 1 find the limits, if they exist. (If an answer does…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: [5-A] [CLO 6] Solve the equation X x +3 + 3 2x-1 = x² - 4x + 1 2x² + 5x - 3

A: xx+3+32x-1=x2-4x+12x2+5x-3

Q: If the lim f(x) and the livigas exist, then the lim [f(x) ga] exists. X-C X-C

A: if the limit x tends to c of f(x) and limit x tends to c of g(x) then the limit x tends to c of…

Q: 12. 5 (S-1)(s-2)

A: As we know from the property of the inverse Laplace transform. L-1a·fs+b·gs=a·L-1fs+b·L-1gs And use…

Q: differential equation x-

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Q: 19. z = ln(x + t²) 21. f(x, y) = X == 23. f(x, y) = y ax + by cx + dy 25. g(u, v) = (u²v – v³)5 20.…

A: 19.

Q: C(x) Find the average cost function C. C(x) = = 1,400 + 7x -0.0002x² (0 ≤x≤ 6,000) Find the marginal…

A: Given query is to find average cost and marginal average cost.

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's 6 √° VI+ Trapezoidal…

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Q: solution not complete, can you upload it again

A: see below the answer required area is in mention as yellow color

Q: The population of a certain state (in thousands) from 1990 (t = 0) to 2000 (t = 10) is modeled by…

A: we need to find out the average growth rate from year 1990 to 2000, also we need to find out the…

Q: how do you justify part b?

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Q: the full answer wasn't shown in the solution box, please provide the rest

A: any differentiable function must be continuous at every point in its domain so  a.) If a function is…

Q: Find an equation for the plane that is tangent to the given surface at the given point. z = √y-x…

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Q: 28. y" - 2y + y = 4x² - 3 + x ¹e*

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Q: the answer on my test corrections is showing 2 with margin:0, could you explain more?

A: To evaluate the following limit. limx→0 sin6xx2+3x

Q: Find the length of the are of the curve y = In over the interval: (1,9. Round the answer to four…

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Q: Find the volume of the solid that lies under the surface z = 3y²x²+2 and above the rectangle R =…

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Q: 45. S sin x sin 2x dx

A: SOLUTION: Question-45: Given that ∫sinxsin2xdx.......(1)  Now we know that…

Q: Evaluate the integral: -28 √7² √² + 100 dx

A: Here we have to find the integration.

Q: Find all points of intersection of the given curves. (Assume 0 ≤ 0 ≤ 2π. Order your answers from…

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Q: 3. For the function g(x) = x³ - 2x² -1, at what tangent point is the instantaneous rate of change…

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Q: Find the derivative of f when 4 f(x) = 6x4 + + 6T. 23

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Q: Use the price-demand equation below to find E(p), the elasticity of demand. x = f(p) = 17,500 - 325p…

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Q: at is the average rate of change between x-2 and x-3 for the function g(x) = 4(x + 1)² -5

A: Given query is to find the average rate of change.

Q: Calculate cos(u) for the following choices of u(x): u(x) = 6 x², cos(u(x)) = u(x) = x=³, cos(u(x))…

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Q: Given f(x)=(1)/(4)x^(2) how did we transform from the parent function?

A: Given f( x ) = 14x2

Q: d²y dy 8. +4- + 20y = -cos 5t dt² dt

A: We need to find out the general solution of the given differential equation,

Q: Write an equation for each graph.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Prove that the radius of curvature of the Helix curve (helical spring) r(t) = (cost,sin t, t) is…

A: r(t) = (cost,sin t, t)

Q: h(x) = 2x²-x-6 x-1 (2x+3)(x-2) (x - 1)

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Q: 9. Given vectors u = [3.-6,8] and =[4.-2.-5]. determine **

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Q: Find an equation of the tangent line to the graph of the function y = f(x), as defined by the…

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