Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, Y, z) = Vx2 + y² + z?, (7, 7, -4) maximum rate of change direction vector

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Q: 4. Let F be a smooth vector field. Show that the flux of F leaving an infinitesimal cube of volume d...

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Q: en k%3D1 00

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Q: х — 1 f(x) = }3x – 3 (-4x + 3 x 3

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Q: The equation x² + 14x + y² – 8y +z2 +10z = – 65 represents a sphere whose center is (-7,4, – 5) |

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Q: dx Evaluate 6e* cos (3e *) -In |sec(3e ) – tan(3e |] + C O 2 [In |sec(3e-x) + tan(3e-)|] + C -18 [In...

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Q: Determine if the given function is continuous at -3. * (x + 7 x< -3 |x – 2|| f(x) = { x² – 2x 9x - 3...

A: Topic:- limit and continuity

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Q: Consider the region bounded by the graphs of y=In x, x=1, and y=1. Which of the following integrals ...

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Q: Determine the value of x of the discontinuous function: * х — 1 = {3x – 3 -4x + 3 x 3

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Q: dy dx + + 3y – 5x – e-t = 0 dt dt dx dy dt + x + y – 3 = 0 dt

A: Given: - The differential equation is, dydt+dxdt+3y-5x-e-t=02dxdt+dydt+x+y-3=0 To solve: - The solut...

Q: Use tables to evaluate the integrals. You may need to complete the square or change variables to put...

A: Topic:- integration

Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the ...

A: Given query is to find the rate of chnage of diameter.

Q: Evaluate the integral. | sin(x) cos(6x) da = +C NOTE: Enter the ezact answer.

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Q: Set up, but do not evaluate, an integral for the volume of the solid obtainedi by rotating the regio...

A: Consider the region   

Q: In each of Problems 1 through 5, determine the canonical form of the eliptic equation. 1. Uzz + 2uzy...

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Q: Find the Maclaurin polynomials of orders n = 0,1, 2, 3, and 4 and then find the nth Maclaurin polyno...

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Q: Choose the angle (in radian) between the following two vectors u = (3, 7, – 8) and v= (-5, 4, - 3) O...

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Q: (х +у—4)dx — (х — у + 2)dy %3D0 -

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Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→...

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: Determine the value of x of the continuous function: * (x – 1 x 3 f(x) = {3x – 3 Зх — (-4x + 3

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Q: 27 dx 1 - 8 ,3 II

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Q: IM: 2. For each of the following series, determine if the series is geometric or not. If it IS geome...

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Q: ............................. ....... ........ ........ ........ ......... Find the volume V of the ...

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Q: 7 B lim f (x)% = 6 T--2- A 2 1(-0.1, 0.5) B2 -7 -6 -5 -3 +2 2 -1 -2 -3 F E 3.

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Q: Use sigma notation to write the Taylor series about x = function. 1 x + 5

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Q: Question 2. Let V = R³, U = {(s + 2t, s, s + t) : s, t E R} and W = {(x, y, x) : x, y E R}. Is V = U...

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Q: flIth)-f(1) find lim.

A: Given query is to find the Indicated expression.

Q: Calculate the definite integral. 4xy Vx2 + y2 dy Calculate the iterated integral. (1 (1

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Q: Evaluate csc?x cot(cot x) dx. O- csc?(cot x) + C O cot(csc? x) + c O -In |sin(cot x)| +c O In sin(co...

A: Given query is to find indicated integral.

Q: and non-real). (Enter your answers as a comma-separated list.) x3 + 12x2 + 46x + 60 = 0

A: Given query is to find the solution of the expression.

Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: Sketch the graph of the given function. Check your sketch using technology. g(t) = (a) Indicate the ...

A: ?As per our company guidelines we are supposed to answer only one question at time or moreover 3 sub...

Q: Solve: |x + 1| > 4 Give your answer as an interval. Question Help: D Video M | Message instructor Su...

A: Topic:- algebra

Q: 1. f(x) = 9-6x 2. g(x)= a. f(-1) a. g(2) b. f(1) b. f(a+b) c. f(3 + x) c. g(2 -x)

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: A spherical balloon is inflated with air flowing at a rate of 15 cm/s. How fast is the radius of the...

A: The formula to calculate the Volume of the balloon is:              V=43πr3 where r is the radius of...

Q: Calculate the iterated integral. r5 CT/2 (y + y2 cos(x)) dx dy -5Jo 120

A: Given query is to find the value of the individual integral.

Q: Question 3: Evaluate the following limits, if they exist, by using the graph 3 -4 -3 -2 -1 3 -1 -2 -...

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Q: Find the area of the shaded region: y y = x - 15 x 20 10 y = x (4, 4) -6 2 4 6. (-4,-4) - 10 - 20

A: QUESTION-  Find the area of the shaded region

Q: Given the General Solution y = ke-0.08x2 Find the value of "k" given the condition (-3, 580). A) k =...

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Q: Graph the curve r = sin(0)+ 1/2

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Q: Evaluate 1 + x2 + y?dS, where S is the helicoid with vector equation r(u, v): 0 < u < 2, 0 < v < T

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Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: (x + 7 |x – 2| x² – 2x x<-3 - 3<x<-1 f(x) = -1<x<3 2х — 3 3<x

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Q: 25. f(x) = 1 – V

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: The function g is related to one of the parent functions described in an earlier section. g(x) = x2 ...

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Q: Consider the following sequence. If the sequence converges, determine its limit. If the series diver...

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