Find the dimensions of the box with square base whose surface area is 20 and volume is maximal   Find the dimensions of the box with square base whose volume is 12 and surface are is minimal

Q: Find the approximate increase by the use of differentials, in the volume of the sphere if the radius…

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Q: We are interested in the first few Taylor Polynomials for the function f(x) = 7e +9e-a centered at a…

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Q: Find the value of the limit for the sequence given. 1-9-17 (9n+1) 0 -1 I 9n+D)} öö (9n)²

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Q: 1. Evaluate: tan 3(x+h) — tan(3x) h lim - h→0

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Q: Eliminate the parameter to express the following parametric equations as a single equation in x and…

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Q: Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

A: To find the Laplace transform of given function

Q: (ii). (x − 3y + 2)dx + 3(x + 3y - 4)dy = 0 - - Ans. In [(x - 1)² +9(y − 1)²] - 2 arctan x-1 3(y-1) =…

A: Let's solve given differential equation.

Q: Use the graph of a polynomial to answer the following questions: A) determine the least degree of…

A: We need to interpret graph.

Q: Problem 9: Solve the following initial value problem: y'(x) = 4 x csc(y), y(0) = //

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Q: ∞ 1 les Σ VR fo To test the series for convergence, you can use the P-test. (You could also use the…

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Q: 07. Given the following function f(x,y)= 3x-x³-2xy². Find, a. All critical points.

A: We need to find critical points and solve function for them.

Q: 2x²ydy where C is the triangle with 7) Evaluate Sexy² dx vertices (0, 0), (2, 2) and (2,0)

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Q: The Taylor series for f(x) = eª at a = -4 is Σ en (x + 4)". n=0 Find the first few coefficients. CO…

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Q: -7 13 Let A = 0 6 Find a matrix S, a diagonal matrix D and S-1 such that A = SDS-¹.

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Q: 6) Show that (2xy, y, 2yz + + x², y²) is conservative.

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Q: $1₁² f(x) dx = -3₁ ["* fo If 1. [² f(x) dx = 2 /*18(x) + 2] dx = f(x) dx = 10, and [8(x) g(x) dx =…

A: If ∫-24fx dx=-3, ∫24fx dx=10, and ∫-24gx dx=8, then to find the following integrals.1 ∫-22fx dx=?2…

Q: (7 points) Consider the region bounded by the curves x = y²-3 and x = y +1 shown below. Set up an…

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Q: 6 6 Suppose f(x) dx = 9 and f g(x) dx = −8. eff (2) d +¡¸g(= -5 -5 6 Evaluate (-2 f(x) + 2 g(x)) dr.…

A: Given:- ∫-56fxdx=9  and ∫-56gxdx=-8

Q: Evaluate the definite integral. S √4x + 3dx

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Q: The two sides of an oblique triangle are measured to be 7 and 9. Find how fast the area of the…

A: given two sides is   7 and 9 given  angle incresing rate is  0.09 radians per seconds when angle is…

Q: Find the absolute error if f(x) = sin(kx) is approximated by truncating its series expansion to…

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Q: Evaluate the following definite intergral. If necessary, round your final answer to three decimal…

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: ∞xk Use the power series f(x) = In (1-x) = -Σ, for -1 <x< 1, to find the power series representation…

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Q: Use the Ratio Test or the Root Test to determine whether the following series converges absolutely…

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

A: dydx=8x16-y2

Q: 2 2x 48. S₁² (15² + 1)² =

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Q: 3 tan xảo 3 xdx secx

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Q: 3. Find the equation of the tangent line to the curve x² + 2y² = 9 at the point (1, -2). Write your…

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Q: The nth term of a sequence is given. n-1 -2-(--/-)² - ¹ an = (a) Find the first five terms of the…

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Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

Q: Find the average value of f(x) = x³ on the interval [3, 5].

A: Given function, f(x)=x3 on [3,5]

Q: 4) Evaluate (¹ + tany)dx + xsec²ydy where C is the curve Y=X²-1 from (1,0) to (2, 3)

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Q: Evaluate the definite integral. Round to 4 decimal places. S™ : dx x√In x Question Help: Submit…

A: To evaluate the integral.

Q: Graph the point with the polar coordinates. -5,- -3) Give two alternative representations of the…

A: Solve the following

Q: Find the first 4 terms of the Maclaurin series function f(x) = Log (1+x), then give an estimation…

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Q: x5 (26 + 6)6 This can be transformed into a basic integral by letting Consider the indefinite…

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Q: Find the derivative of f at point P in the direction of u.

A: Given,            fx,y,z=cos3xy+e8yz+ln7xz ,P=3,0,4 , u→=8i+6j+5kTo find : Find the derivative of f…

Q: The dimensions of a box are x, x + 14, and x + 17. Find how fast is the volume of the box increasing…

A: The dimensions of the box are: x,  x+14  and  x+17Now the shotest edge is: xTherefore: x=12

Q: Solve the following maximization problem graphically. Subject to: P(x, y) = 38x6y + 14 x + y ≤ 10 2x…

A: To solve the following maximization problem graphically.Px, y=38x-6y+14 subject to:…

Q: The x-intercept of the tangent line to the curve y = x - 6 / x at the point (4, 4) is:

A: Given,           The curve is y=x-6x and the point is 4,4.To find : The x-intercept of the tangent…

Q: A torus of radius 10 (and cross-sectional radius 1) can be represented parametrically by the…

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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: Find the linear approximation to the equation f(x, y) 5 approximate f(4.11, 6.23). f(4.11, 6.23) xy…

A: formula for linear approximation is  f(x,y)=f(x0,y0)+fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0)given…

Q: 3. [2] A company manufactures mountain bikes. The research department produced the marginal cost…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 4n²+3…

A: Let's find  given series is convergent or divergent.

Q: Find the gradient of U = 2p(z² + 1) cos p. ○ 2sin (4) (z²+1)a − 2cos(p) (z²+1) a + 4pzcos(p)a 2cos…

A: Given U = 2ρ( z2 + 1 )cosφ

Q: Find the slope of the parametric curve x = -3t² +8, y = 6t3, for-co<t<∞o, at the point corresponding…

A: slope is  =dydxand we know that  dydx=dydtdxdtdtndt=ntn-1,   and   dconstantdt=0

Q: 1 Find the divergence of U = r cos 0 ar sin 0 a + 2r² sin α- 0 ap. r O None of the choices O O O 3…

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Q: For what value of k will the function f(x) => =X k - X have a relative maximum at x = -1?

A: To determine the value of k for which the function fx=x-kx have a relativemaximum at x=-1.