Find the divergence of the vector field F =< yx³, xz¹, zy³ > div F =

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Q: Find Duf at P. 1 f(x, y) = 3(1 + xy) ³/²; P(3,1); u= NOTE: Enter the exact answer. Duf = S i+ j

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Q: tan² x - cot² x - = sec² x csc² x

A: tan2x – cot2x = sec2x – csc2x Verify the Expression.   Pythagorean Identities : sec2x = 1 + tan2x…

Q: 5. Given the graph of f'(x),answer the following about f. . Critical number(s) of f (where f' = 0 or…

A: Given graph of f'(x) is:

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Q: A graphing calculator is recommended. Use a calculator or computer to find the length of the curve…

A: According to question,Given Curve,r = cos 2θ

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A: We need to find function in given form.

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A: Given: f(x) is continuous on 2,7 and -4≤f'(x)≤3 for all x in 2,7 We are required to: Estimate the…

Q: Perform the indicated operation and write the answer in the form of a +bi. (6+5)-10i O -5+6i O 6+5/…

A: let  K=(6+5i)-10i

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Q: +V X find dy/ dx tan (cos x)

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Q: Use linear approximation, i.e. the tangent line, to approximate √27.3 as follows: Let f(x)=√x. The…

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A: To find the area of the region bounded by the given curves, we need to set up the integral in polar…

Q: Evaluate ₂ ₁ 32r³y³dxdy.

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Q: e 1. calculate the following limits. If the limit ends lim x-30x ends up boing + ∞o, 2 (1) ex-1

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A: Given that,  The volume of the cylinder = 200 cubic centimeters. The sides and bottom of the…

Q: Consider the function f(x) = 2x³-9x²60x+2 on the interval [-4, 7]. Find the average or mean slope of…

A: fx=2x3-9x2-60x+2

Q: 1. 2. 5x If A(x) = Son O ^(1/3) = A¹(4)- 1 1 + f² Jt then:

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Q: Ex 15.5.13 An object occupies the volume of the upper hemisphere of x² + y² + z² = 4 and has density…

A: We have to find the center of mass of the object.

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Q: Consider the following descriptions of the vertical motion of an object subject only to the…

A: it is given that,  the gravity of the earth is g=-9.8 m/s2

Q: Find f given ƒ' (x) = 2x - 10/8/ 5 x6, x > 0, ƒ (1) = 3

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Q: Find the gradient vector field of f(x, y) = ln(6x + 3y)

A: given  f(x,y)=ln6x+3ywe know that→(i)  ∂ ∂x(xn)=nxn-1(ii)  ∂ ∂x(lnx)=1x

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A: Given: We are required to find: a.∫023f(x)dxb.∫063f(x)dxc.∫143f(x)dxd.∫162f(x)dx

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A: The answer is in next step.

Q: Let f be the function defined by f(x) = . What is the approximation for f (10) found by using the…

A: f(x)=x3 Find the first derivative of the given function  f(x)=x3=x13f'(x)=13x13-1......(Since,…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

A: vt=3t-7, 0 ≤t≤3 Graph

Q: Consider the function f(x) = 10√x+6 on the interval [2, 5]. Find the average or mean slope of the…

A: According to the mean value theorem  f( x ) in interval [ a , b ] f'( c ) = f( b ) - f( a )b - a…

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Q: 1 2. Does the series Σn=11 converge or diverge? Give a concise explanation 2n 3. Does the series…

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Q: 4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: The sum of two positive numbers is 16.

Q: If a rock is dropped from a height of 215 ft, its poistion t seconds after it is dropped until it…

A: Given :st=-16t2+215

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Q: Let f be the function defined by f(x) = 1+x²/3. onsider the following properties: A. has local…

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Q: Consider the function f(x) this interval. 1 = on the interval [3,9]. Find the average or mean slope…

A: Consider the function fx=1x on the interval 3, 9. To find the average or mean slope of the function…

Q: 1. Evaluate. a. b. arctanx e dx 0 d arctanx Se dx dx dx

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Q: Does the series Σ n=1 n+1 converge or diverge? Choose the correct answer below. *** A. The nth-term…

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

A: By using the definition to find an expression for the area under the graph of f as a limit.…

Q: Find f. f(x) = f"(x) = 6 - 6x - 40x³, f(0) = 5, f'(0) = 7

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Q: Flight of a Rocket The altitude in feet attained by a model rocket t seconds into flight is given by…

A: Given,          The altitude in feet attained by a model rocket t seconds into flight is given by…

Q: The function w() is graphed below. Find the value of each of the following integrals based on the…

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