Q1 :  a) For the function f(x )=x^3 −12x, its local maximum is ____?____ which occurs at (___? __ ; its local minimum is  ____?____  which occurs at (___? __ ;

Q: 2 Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and x = 3,…

A: we have to find the volume abouts y-axis

Q: Given the vector u = (-5,4), find the magnitude and angle in which the vector points (measured…

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Q: n constructing an open rectangular box from 1323 ft² of material, what dimensions will result in a…

A: NOTE: Refresh your page if you can't see any equations. . x=length of the box y=width of the box…

Q: Find the equation for the tangent plane to the surface z = 9x² - 6y² at the point (2, 1, 30). OA.…

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Q: Find the intervals on which the graph is concave up and concave down. (Enter your answer using…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = -5x² - 2xy-4y²…

A: To find all local maxima, local minima, and saddle points of the following function. fx,…

Q: A plate in the shape of an isosceles triangle with base 1 m and height 8 m is submerged vertically…

A: A plate in the shape of an isosceles triangle with base 1 m and height 8 m is submerged vertically…

Q: Use the theorem given below to find the curvature of r(t) = √62²i + 2tj + 2t³ k. k(t) = Theorem: The…

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Q: distance in between the point P(3, 1, 2) and the point Q(0, 4,

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Q: Write an iterated integral for and x = 243 using a. vertical cross-sections, b. horizontal…

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Q: Two particles start at the origin on the s-axis at time t = 0 s and move along the s- axis. Their…

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Q: Find a formula for the n" partial sum of the series 5- th The formula for the nth partial sum, s of…

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Q: Q8 Find the slope at x = 2 on the graph of f(x) (a) -3 N/W (b) 3/3 (c) 3 4 = 3 (d) 0

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Q: f- 3 2 (x"+x"-x-1)dx x+1

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Q: Determine h (x²) for the following function. h(x) = 4x x² - 4x + 5

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Q: You are designing a 1152 cm³ right circular cylindrical can whose manufacture will take waste into…

A: We use the differentiation method to find the required ratio

Q: Use calculus to find the area A of the triangle with the given vertices. (0,0) , (4,3) , (1,8)

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Q: Find the average value of F(x,y,z)=x² + y² + z² over the rectangular solid in the first octant…

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Q: h(x)=5.5x-3.42

A: We have given a polynomial  hx=5.5x-3.42 Leading term =5.5x

Q: J xlnxdx X X

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Q: Find f.  F"(x) = t2 - 4

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane y + z…

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Q: We can represent planes using either vector equations or scalar equations. Which form do you think…

A: We have to answer which form of plane is better Either vector or scalar

Q: Given (y)-16-²-², use the total differential to approximate or at (4.1) towards (24,1.05). Round…

A: △x=2.4-4=-1.6△y=1.05-1=0.05

Q: avaries directly as the square of band inversely as the square of c. If a = 89 when b = 6 and c = 6,…

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Q: Find the derivative of the function at the given point in the direction of A. f(x,y,z)=2x-4y+7z,…

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Q: Find the extreme values of f(x,y) = xy subject to the constraint x² + y² -4 = 0. The extrema are…

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Q: Using the equation y= x^3/ x^2 - 4 Determination of equations of horizontal asymptotes (if they…

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Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: Using the equation y= x^3/ x^2 - 4 Determination of critical numbers for the first derivative test…

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Q: Find the extreme values of f(x,y) = 4x + 6y subject to the constraint x² + y² = 13. 2 OA. The…

A: Question Find the extreme values of f(x,y) = 4x+6y subject to the constraint x2+y2=13

Q: Use the following identity to evaluate the given integral, shown below. 1 sin mx sin nx= [cos…

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Q: Find the surface area of revolution about the 3 y-axis of y = 10x over the interval 4 0 < x < Enter…

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Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 - Find the differential dy when…

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Q: Hi, Can you be so

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: Find a plane containing the point (-3,6,-4) and the line x (t) = y(t) z(t) = = - 4 - 8t - 6-7t - 2 +…

A: I have solved step by step in detail...go through the solution

Q: metal Bar at a temperature of 120°F is placed in room temperature 10F, If after 20 mins, the…

A: Given: T1=temperature of the metal bar, 120°FT2=room temperature, 10°FT=temperature of the metal bar…

Q: Suppose that f(x, y) = z²y. The directional derivative of f(x, y) in the directional (-1,-2) and at…

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Q: Q12 Construct the equation of the line passing through (0, -2) and (3,5).

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Q: Name the method by determining whether I'Hôpital's Rule should be used or not. CSC x lim x+0+ √x

A: Need to write down the method to determine that l hospital is applicable or not.

Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

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Q: Express the sequence {an} n = 1 as an equivalent sequence of the form {n}=4* n=1 {2n +5}=1 ∞ An…

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Q: Find the centroid of the region cut from the first quadrant by the circle x² + y² = 81.

A: Find the centroid of the region cut from the first quadrant by the circle x2+y2=81.

Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

A: Given, f(x, y) = e-xyRegion, x2 + 4y2 ≤ 1   Finding the critical points, ∂f∂x = -ye-xy∂f∂x = 0, y =…

Q: -1 If ƒ(x) is a positive 1-1 function with inverse ƒ−¹(x) with f(a) = c and ƒ(b) = d then d π ñ ["°*…

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Q: Find the value of each of the six trigonometric functions (if it is defined) at the given real…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A: Given: y = 4x2 x = 1  y = 0 about x-axis

Q: The vectors [.. -9 are linearly independent if and only if k # ū -4 4 13+ k_ " -3 7 16

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