16 Evaluate ex12 (x4 – 2x² + 1)²dx. 81

Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the s...

A: We need to find dimension of an open box that maximizes the volume.

Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to th...

A:

Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

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Q: b) E(-1)"+1 Vñ Inn n-1

A: The given series is: ∑n=1∞nln n which is an alternating series with bn=(-1)n+1nln n, n≥1  

Q: 3. Evaluate all the first partial derivatives of the given functions at the given point. of of 1 a) ...

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Q: Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint...

A: We can solve both the part as below as per the instructions of Professor Lapan's Helpful Hint:.

Q: Let S(z) = {-3z? + 5z for z 0. 3z2-2 According to the definition of the derivative, to compute f'(0...

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Q: How much money must you invest now at 4.5% interest compounded continuously in order to have $10,000...

A: We know continuous compounding formulaP(t)=P0ert where value at time t P0=principal amount r= annual...

Q: - ydx + x(Inx – Iny - 1) dy = 0, when x = 1, y = e %3D

A: Let's find. 

Q: Use Integration by parts to aompute the ntegral from! (4x)dx and 3 Inxdx

A:

Q: Find the minimum speed of a particle with trajectory c(t) = (t,14) for t 2 0.5. (Use decimal notatio...

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Q: Express the surface area of revolution for: x = (y^4/4) + 1/(8y^2), 1 ≤ y ≤ 2; x@axis ( Express ds= ...

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Q: Evaluate the following:

A: Given that: ∫(6x2-4x+1)dx

Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

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Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter wi...

A: Solution of the problem as follows

Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2 ...

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Q: .3 dx S (x4+ 16)' 2

A: This question is based on indefinite integral.

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: Given P(x) = x³ + 2x? + 4x + 8. Write P in factored form (as a function with a product of linear fac...

A: Given p(x)=x^3+2x^2+4x+8.

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

A:

Q: For the function y - f(x)- 2x + 0: df at = d.x a. Find 4. f'(-4) = 96 b. Find a formula for a 1 df a...

A: Answer: a.) ddf(2x3+0) = 6x2 =f'(x)f'(-4) = 6×(-4)2 = 96   b.) y = f(x) = y = f(x) = 2x3 + 0y = 2x3 ...

Q: sin(tan-1))

A: SOLUTION-

Q: 2x+9 10. S x2+6x-4

A: Follow the procedure given below. 

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given m...

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Q: Evaluate thu Integral IF the funcion x = rectongular flaiy) = xSin (x;y) %3D over the region R- [0,m...

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Q: Based on the graph, fill in the table with the appropriate values lim f(x) f(c) -2 -1/2 1 3 4

A: Given

Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper frac...

A: To determine the sum of the following series.71⋅3+72⋅4+73⋅5+ ...  

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: (х — 2)(г + 2)( +1) (х + 3)(ӕ + 1)

A:

Q: The size of a certain insect population is given by P(t)=400e population equal 2000? 011 where tis m...

A: Given that: Size of population at any time t, P(t)=400e0.1t

Q: Provide an appropriate response. lim f(x+ h) – f(x) Find the difference quotient, for the function f...

A: Please see the answer below.

Q: Use implicit differentiation to find y' and then evaluate y' at (3,4). 8x? - y° - 8 = 0 y' =D y'l(3....

A: The given function,      8x2-y3-8=0

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given problem:- Use a linear approximation (or differentials) to estimate the given number. (1.999)5

Q: b) y = 1 - v 1 + v2 -82 dv dy = 1+v

A:

Q: The temperature T (in °C) at a location in the Northern Hemisphere depends on the longitude x, the l...

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

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Q: Find equations of all lines having slope - 1 that are tangent to the curve y = x-8 Select the correc...

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Q: Write the first five terms of the sequence, give the exact answer: +oo In+11) n=1 Determine whether ...

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Q: 35-40 Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the ...

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Q: Determine whether the integral is convergent or divergent. The integral from 0 to 9, 7/(x-1)^1/3 dx ...

A: The integral is  ∫09 7(x-1)1/3dx

Q: Inx 2. lim x-1x-1 1 0.9 0.99 0.999 1.001 1.01 1.1 f(x)

A: Find your answer below 

Q: 21. 22. (D' + D - 9D' – 13D² + 8D + 12)y 0. Ans. y Ce+cze

A: We will solve the given differential equation.Below find the solution in the image.

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. 7" Σ ...

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Q: Let f(x) = x' cos ( x-) and calculate ed S(x) dx by using integration by substitution. What was your...

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Q: (a) What is the rate of change of f(æ, y) = 2xy + y² at the point (2, 1) in the direction i = –3i – ...

A:

Q: 3.

A: Given that, There are two equilateral triangle. Area of small triangle is 64(3)1/2 m2. Distance betw...

Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 - ...

A:

Q: The reverse variation formula where x is the nonzero independent variable y is the dependent variabl...

A: The  reverse variation formula

Q: Determine whether the integral is convergent or divergent. The integral from 0 to 11, 1/(11-x)^1/3 d...

A: The given integral is  ∫011 1(11-x)13dx  

Q: %3| Find the value of k if the f(kx2 – 2x + 3)dx = 14.

A: Definite integration