remains positive. It is modeled by the function e-t. alue of in the long run.

Q: Q4. Find the arclength of the curve given by the equation r(t)= (5 cos t², 5 sin t2,12 t²), for 0 ≤…

A: formula for arc lenth is  L=∫ab(dxdt)2+(dydt)2+(dzdt)2dtgiven x(t)=5cost2         y(t)=5sint2…

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A:

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A:

Q: Find the average value over the given interval. y=4e-x; [0,4]

A: Given query is to find average value of the function.

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A: Given f'( x ) = f( x ) ( 1 - f( x ) ) f( 0 ) = 110

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A:

Q: Solve the initial-value problem y' = (8 sin(x))/sin(y), y(0) = π/2.

A: Topic = Differential equation

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A: We need to find volume.

Q: 9. Find the derivative of A) B) y = (lnx)4 y = ln x4

A: we know that  lnxn=nlnx dlnxdx=1xA)   given   y=(lnx)4

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Q: O dx √4-9x² O -1 sin O 1 sec sin 0 1 3 -sec 3x 2 2x 3 2x 3 + c + c +c 3x ¹ (³2) +c

A: Integral

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A: As we know that, The Power Law: ddxxn=nxn-1   To calculate the limit limx→1lnxx7-1.

Q: Thanks

A:

Q: Use series to approximate the definite integral I to within the indicated accuracy. · (four decimal…

A: Here, notice that the series of…

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A: Given integral:- ∫x5x6-67dx

Q: -10 -5 9 6 3 -6 -9 y X 10 a Write the standard equation for the hyperbola graphed above.

A:

Q: Find the area enclosed by the line x = y and the parabola 4x + y² = 12.

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Q: Use the given information to find the unknown value. y varies inversely with the cube of x. When x =…

A: Given a relationship between y and x

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A: Given that 28 pizzas are ordered in total and they costed $246 in total.

Q: 4. 16x²-x+3 6x²-5x2+1

A:

Q: ³ f(42° +22³) dz Find + C

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Q: x=5t²+2t _y=2+²+4

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Q: Find the area of the region bounded by the graphs of the given equations.   y=2x2−5x+5​; y=x2+7x-15

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Q: Write the first five terms of the geometric sequence whose first term is 2, and whose common ratio…

A: Find the first five term

Q: Question 3 of 12, Step 2 of 2 Consider the function: f(x)=(x²-4)² Step 2 of 2: Use the Second…

A: Please see the below picture for detailed solution.

Q: Find the height of the right circular cone of largest volume inscribed in a sphere of radius 50.

A:

Q: Let f(x, y) = x6y7. Find the linearization L(x, y) of f(x, y) at the point (1, 1). L(x, y) = Find…

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Q: mRNA is an intermediate molecule that arises in the decoding of DNA. mRNA is produced by a process…

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Q: Solve the given differential equation. dy dx -8x√16-y2 = (A) y=sin (4x² + C) (B) y=sin¹ (4x² + C)…

A: To find the solution.

Q: Find the sum of the series: n=0 x³n-2 n!

A:

Q: 2) The solid S consists of the points above xy-plare, below cone x²+y2=2², enclosed by the surfues…

A: According to question,Given cone,x2 + y2 =z2,Given Surfaces,y = x,x = y2.

Q: 5) Find the divergence of (√x² + y² + )(i + y + zk)

A:

Q: •πT (2sinx + 3cosx + 1)dx

A:

Q: Compute the percent relative error in computing the area of a square whose side is measured with an…

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Q: The normal line at x = 4 of the curve y=x²+x+, where m= 3 and n = 0, interects the curve at a second…

A: I have solved step by step in detail...go through the solution.... I have used two perpendicular…

Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(1). f(x) = -3x - 14 g(x) =…

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Q: available rest Estimate the area under the graph of the function f(x)=√x+6 from z=-3 to z = 5 using…

A: The given function fx=x+6 from x=-3 to x=5. We have to find the area under the graph using midpoint…

Q: M: Solve b- - 2 ²2-d+ 2y = 3e*

A: We use techniques of higher order linear differential equations to solve the given differential…

Q: Evaluate the indefinite integral. 2²√14+ rºdz + C Question Help: Video Message instructor Submit…

A: ∫xndx=xn+1n+1+clet  A=∫x214+x3dx

Q: Find the average rate of change of the function over the given interval. P(0)=03-302 +60; [1,2] ΔΡ…

A: use the unction value at given interval or finding the average rate of change .

Q: Find the indefinite integral on the domain of positive real numbers. Enter an exact answer. Remember…

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Q: b- day-22 dx3 2022 - 2 +2y = 3ex d²y dx

A:

Q: Let an = n/(n + 1) and L = 1. Given a tolerance of 0.01, find an integer N such that TL 20.01 for…

A: Please see the below picture for detailed solution.

Q: Solve the differential equation. dz dt + 3et+ z = 0

A:

Q: If x units of a certain item are manufactured, each unit can be sold for a-bx pesos, where a = 184…

A: Given sell function s( x ) = a - bx where a = 184 & b = 0.52 s( x ) = 184 - 0.52x

Q: what is the answer to d?

A: Please see the below picture for detailed solution.

Q: Find how fast the volume of a parallelepiped is increasing if its edges a, b, and o change at rates…

A: According to question,Given Edge of parallelopiped,a= 5,b = 6,andc =10,Rate of change of It's…