Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

Q: Find the indefinite integral. [Hint: Use some algebra first.] (Use C for the constant of…

A: ∫t-2t+6t2dtExpand:=∫4t-12t2+1dt=4∫1tdt-12∫1t2dt+∫1dtWe know that ∫tndt=tn+1n+1

Q: With your pencil, make a dot on the position of your best visual estimate of the centroid of the…

A: Here, from the given data, it is clear that the centroid is on the y-axis. So, the x-coordinate of…

Q: Find the solution to y' =    2y satisfying y(0) = 15.

A: Solve the following

Q: If f(3) = 5 and f ′(x) ≥ 2 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: 5. Evaluate each of the following inte x² (53+1)3 (5 (a) da

A: We have to find the solution As per guidelines we have to solve one question Please repost other…

Q: Find the critical value(s) of f(x) = 7√x – x², to two decimal places as needed. Separate multiple…

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Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

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Q: The base of a three-dimensional figure is bound by the line x = -y - 2 on the interval [-5, -2].…

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Q: Let R be the region bounded by y=x², x=1, and y = 0. Use the shell method to find the volume of the…

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Q: lim X→∞0 lim x118 √11+4x² 2 + 11x √11+ 4x² 2 + 11x = =

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Q: The following chart shows student population in a certain elementary school over a 5 year period.…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question can be solved using the concept of parametric and symmetric equation of lines in three…

Q: Determine the area bounded by x2= 4y and y= A B C D E 4 π-- sq. u. 3 2A- - 4 3 sq. u. -- sq. u. 133…

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Q: 2).  Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic equation for C =…

A: Given problem:- Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic…

Q: Find the total change of f(x) between x = 1 and x = 3, when df = 3x² + 2x

A: NOTE: Refresh your page if you can't see any equations. . here we have the given values of x are…

Q: Use the Ratio Test to determine if the series converges. 10k k=1 Select the correct choice below and…

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Q: Find the general solution of the given ODE ( 40² – v) dx + x dy 0.

A: The given DE is: (y2-y)dx+x dy=0⇒(y2-y)dx=-x…

Q: Find the derivative of f(x) = 8 In (2). Enclose arguments of functions, numerators, and denominators…

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Q: 11) Find the general solution to the differential equation. y' = eyx2

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Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: Evaluate the following limit using L'Hospital's rule. limx→∞ x2+3x+12 / 6ln(x3

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Q: Problem 18. Sketch the region enclosed by the given curves. Decide whether to integrate with respect…

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Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…

Q: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

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Q: 4. The associated auxiliary equation with the homogeneous linear differential y"+2y' + y = 0 is A.…

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Q: If f(x) = 4x² - 4x + 4, find f'(3). Use this to find the equation of the tangent line to the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: A soccer ball is kicked into the air, and its height (h) in feet after t seconds is given by h( t )…

A: A soccer ball is kicked into the air, and its height (h) in feet after t seconds is given by…

Q: Use the Ratio Test to determine if the series converges. 10k Σ k=1 Select the correct choice below…

A: The given series is ∑k=1∞10kkk

Q: II. Solve the given linear differential equation showing the details of your work. 1. (D²…

A: The given differential equations are;  1) (D2-3D+4)y=16x-50Cos2x 2)(D2-3D+2)y=Sin(e-x).

Q: 3x + 8 Consider the function f(x) = . For this function there are two important intervals: (-∞, A)…

A: Find out the value of A at which the function is not defined.

Q: Find the limit. 3x3 lim (x,y) →(1,-2)1+x2 00 0-12120 O 1 ula 0-1/105 O

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Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = y³ - 9x²y x = es, y = et…

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Q: Suppose the formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74…

A: answer is in next step . please give a like !!

Q: Find the 11th term of the following geometric sequence. 2,8, 32, 128, ...

A: This question can be solved using the formula of general term of geometric sequence.

Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: volume is described as follows: 1.  the base is the region bounded by y=4−4x^2 and y=0 2.  every…

A: answer is in next step.

Q: Let f(z) = (9 sin z + 2 cosz)tan¹z

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Q: At which of the marked values of x is A. f(x) greatest? x = B. f(x) least? x = c. f'(x) greatest? x…

A: Note:- According to company guideline we can do maximum 3 sub parts so i am solving here first 3

Q: Work Problem 3 (.. : b) Using the Lagrange multipliers method find the extreme value(s) (if it…

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Q: Consider the function f(x) = 12x5 + 15x¹ - 240x³ +2. f(x) has inflection points at (reading from…

A: Consider the function fx=12x5+15x4-240x3+2.fx has inflection points at reading from the left to…

Q: Determine the values of where the function f(z) is not continuous. Label each discontinuity as…

A: Solution of given question is written in below steps.

Q: Find the absolute extrema for the given function on the interval [1.2, 3.7]. Write your answer in…

A: The given function is fx=5x4ln x on the interval [1.2, 3.7] we have to find its absolute extrema.

Q: Let 14 f(x) = (3x²-5) 5 (- 5x² +9) ¹4 f'(x) = > Next Question

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Q: Find the directional derivative of the function at P in the direction of v. √2 2 f(x, y) = x³ - y³,…

A: Given problem:- Find the directional derivative of fx,y=x3-y3 at point P8,3 in the direction of…

Q: runner

A: A runner is jogging at a constant speed of 3.9 miles per hour. a.) If d(t) is the distance the…

Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

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Q: Partial fraction decomposition can now be used to write L{y}, such that all terms have linear…

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Q: Find the second derivative of f(x) = 7 sin(4x). Enclose arguments of functions in parentheses. For…

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Q: Find the solution to y' =    2y satisfying y(0) = 15.       PLZ SHOW STEPS

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