A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 64 – x2. What is the largest possible area (in squared units) of the rectangle? squared units

Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: FInd Fas a function of x and evaluate it at x = 0, x = 7T/3, and x = /2. FX) = F(x Cos 8 de Fx) FO)

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Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

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Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: (H.W) 1- Solve by choose M this time ( 2 x y² + 3 x² ) dx + ( 2 x² y + 4 y³ ) dy = 0 2- Find the…

A: If the differential equation Mdx +Ndy =0  is exact ∂M∂y=∂N∂x , then solution is                 ∫y…

Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Write the nth term and  add them to get Sn .

Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function F(x) = x…

A: A complete solution is given below.

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: (D² +1)y = sec x. %3D

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Given query is to find the series converges or diverges.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: dx cos4 6x

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Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Let's find.

Q: Determine if the following series converge: 2.4.6 . · (2n) ... (a) (b) ) Inn 3.6 - 9 · · · (3n) ...…

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Q: Cives f(x.g) = メー2メラーリメy+5 Find the Ccritical points oo f and all detevmine the nature of each of…

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Q: Calculate the power series solution of the differential equation of y'- y= e* up to the five terms.…

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Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: - sin² ydy 6. 4 tan" y

A: As per the guidelines I can solve only first question

Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: S(Vcos x + sin x)´dx

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Q: Solve the equation cos? x - cos x = 0 over the interval [0°, 360° ]. solving for cosx, solving for…

A: We will solve for cos x and x.

Q: Give inequalities for r and 0 which describe the region below in polar coordinates. (Click on the…

A: Angle is given by arctan(y/x)

Q: S cos³ 3x dx

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Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: ind 4 using implicit differentiation and evaluate the derivative at point (-1,2) 2.a°y + 5x?y³ = 2x

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Q: find the first partial derivatives of the given function. complete solution z= 3x2y - y3 + 4x - 7

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Q: In x

A: A detailed solution is given below

Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 4.…

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Q: 3 lim (1+ 4 x2

A: Given query is to find the limit of the expression m

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

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Q: Find the are lengtu of tue graph 10) of the fenetian y= x+5 over the imiterval [12, 14]. Anwens a) §…

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Q: answer

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Q: Let g(z) = / ft) dt, where f is the function whose graph is shown below. What is the value of g (8)?…

A: We have to find value of g(8)

Q: no1

A: Topic:- application of derivatives

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: s @ = 135° a solution to the equation sine = cos 0. Justify your answer and explain the approach you…

A: Given query is to find that statement is true or not.

Q: Solve the triangle. Round your answer to the nearest tenth. mZA = 37°, a = 28, с 26 mZB 109°, m2C =…

A: Given query is to solve the triangle.

Q: Evaluate the limit using L'Hospital's rule if necessary sin(4x) lim z→0 sin(6x)

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Q: 15. Find x² (2x³ + 4)5 dx

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Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…