Given the function f'(x) = −x³ – 6x² + 72x, determine all intervals on which f is decreasing.

Q: Consider the following vector field. F(x, y, z) = 4yz lnxi + (3x − 7yz)j + xy6z³ (a) Find the curl…

A: given vector field

Q: Qestion 2 a). Use vector projection to explain the distance in part (iii) equation b). find the…

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Q: Find the values of x so that the series below converges. Give your answer in interval notation. n=0…

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Q: Differentiate the following function. √√/2²2² +4√√/13³ u u'(t) = || X

A: u=5) +4 sqrt(t3)

Q: How many minutes does it take John to type y words if he types at the rate of x words per minute?…

A: Given,John types x words in 1 minute Find :- Number of minutes does John take to type y words

Q: Given: (x is number of items) Demand function: d(x) = 762.3 – 0.2x² Supply function: s(x) = 0.5x²…

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Q: The manager of a 100-unit apartment complex knows from experience that all units will be occupied if…

A: Given Information - If the rent is $700 then all 100-unit apartments of the complex will be…

Q: Compute the directional derivative of the following function at the given point P in the direction…

A: To Compute the directional derivative of the following functions at the givenpoint P in the…

Q: A triangular plate with height 6 ft and a base of 8 ft is submerged vertically in water so that the…

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Q: If you wish to integrate a function over the top half of the unit ball using spherical coordinates,…

A: The objective of the question is to determine the range of the spherical coordinates θ and φ when…

Q: (2) For what value of c does y = cx + have a relative minimum at x = 2? (A) ³/ (B) (C) 0 (D) 2

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Q: Consider the series. -7/12 +49/144 - 343/1728 +2401/20736 + ... Determine whether the series…

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Q: Find the derivative of the function. f(x) = (2x3)4(x² + x + 1)5 :- 3) ³ ( x² + x +: f'(x) = (2x-…

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Q: A. Use the Maclaurin Series with n=4 to approximate cos(2.1) to 4 decimal places. B. Using your…

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Q: 16-t -t6 -dt t4 Integrate: /M + C

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

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Q: Which represents the correct difference quotient for the function f(x)=4x²-3x+2? A B C D f(x+h)-f(x)…

A: Here we have given a function :

Q: Use Newton's method to estimate the two zeros of the function f(x)=x-x-2. Start with x= -1 for the…

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Q: Determine the general solution. y"-3y'+2y=2x2+1

A: given differential equation

Q: Below are four sets of ordered pairs. Identify each using the following: n = the set of ordered…

A: Given that n = the set of ordered pairs does not represent a functionf = the set of ordered pairs…

Q: Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find f(x) if f"(x) = 24x²+2x+8, f(0) = 5, f'(1) = -2.

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Q: Lets (t) = 51² - 24t be the position function of a particle moving along a coordinate line, where s…

A: Given,

Q: Evaluate the integral: O x = (A) Which trig substitution is correct for this integral? 7 X = x = x =…

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Q: Current Attempt in Progress Incorrect. Find the area under P = 120(0.7)' between t = 0 and 1 = 6.…

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Q: Find the relative rate of change of f(x) = 12 +2e-2x The relative rate of change of f(x) is

A: Relative rate of change of f(x) can be expressed as the slope (or first derivative) f'(x) of a…

Q: g(x) = * (4 + sin(t)) dt

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Q: Click on the graph to view a larger graph Use the Law of Cosines to find the indicated angle a given…

A: given triangle ABC

Q: x = 3 cost, y = 8 sint; 0st≤ Determine the rectangular equation of the curve. Choose the correct…

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Q: Verify Green's Theorem by evaluating both integrals an √ 7² dx + x² dy = √ √ √ (²x- ax for the given…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Given that the region bounded by the curves

Q: For what values of p is each series convergent? n = 1 (-1)^-1 np +2

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Q: stion a). Use the geometric definition of to explain the distane equation cross product in part (1)…

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Q: Tutorial Exercise An oil refinery is located on the north bank of a straight river that is 1 km…

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Q: i would like to know how to calculate this without a calculator or big numbers

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Q: The size P of a certain insect population at time t (in days) obeys the function P(t) = 300e0.071…

A: The insect population is given by, where t is the number of days.The aim is to find the number of…

Q: How would I set up an integral that funds the volume of the cylinder?

A: This is question of calculusHere we have to find step for calculate the area of cylinderFurther…

Q: Find the relative rate of change of f(x) = 12 +2e-2x The relative rate of change of f(x) is

A: The objective of this question is to find the relative rate of change of the function f(x) = 12 +…

Q: Graph the polynomial P(x) = x³ + x²-5x + 3 using calculus by showing the given st (e) Sketch the…

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Q: Find the Left Riemann Sum and the Midpoint Riemann Sum for the function f(x) = x² - 2x on the…

A: The given function is .The aim is to find the left Riemann sum and the Midpoint Riemann sum for the…

Q: A particle is moving in straight line and the velocity at time t is given below: v(t) = 2-2t. Find…

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Q: Find a basis for the solution space of the given homogeneous linear system: a-3b+2c-4d=0…

A: Find a basis for the solution space of the given homogeneous linear system:a-3b+2c-4d=02a-5b+7c-3d=0

Q: Evaluate the following. [³√9+xªdx 9 + x4 dx

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Q: (6) A piece of ice cut in the shape of a cube melts uniformly so that its volume decreases at 3…

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Q: Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: 5. *²2²√25 - 2²³dz

A: The given integral is

Q: Sketch the graph of the quadratic function. f(x) = 3x² + 2 No Solution Help -10 9 8 7 6 5 4 3 2 -1…

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Q: Find the volume of the given solid region in the first octant bounded by the plane 4x + 8y + 2z = 8…

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Q: Find a basis for the 2-dimensional solution space of the given differential equation: y" - 5y' = 0

A: The given differential equation is