Examine the function for relative extrema and saddle points f(x, y) = x³ 3xy + y³

Q: (7) Function f(x) is defined as y = sin x + ln x, Note that x and y are functions of t. Find…

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Q: Use the graph below to find the indicated limits. If a limit doesn't exist, state DNE. If value…

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Q: Sa J x² e ³x dx 3x

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Q: Draw a sketch of the graph of f(x) = 2√x + 1 − 1. Explain the trans- formations of the graph of…

A: Explaination of the answer is as follows

Q: Find the total solution to the initial value problem: y" + 4y + 4y = 2e-2t y (0) = 1, y' (0) = 1…

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Q: Question 3. a. Use Cramer's rule solve the following system for x and y b. Let A - ( ₁ = 4 1 x - 2 x…

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Q: 5. Given a = 47 - 7k in R³, determine a) a in component form b) la (exact value)

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: As per the guidelines, I am providing the solution to the first question.

Q: a. f(x) = F ť² — b. f(x) = = 1 X-1

A: Given that function:  f(x) = 1/x2 - 1 and f(x) = 1/(x-1).Determine the flat asymptote of this given…

Q: Thanks for answering. That one was correct . Please could you also answer the second one?

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: dy Solve the given differential equation by using an appropriate substitution. The DE is of the form…

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Q: A cable that weighs 4 lb/ft is used to lift 800 lb of coal up a mine shaft 550 ft deep. Find the…

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Q: d'y dx² when x = 2 and y = 4. If 4x² + y² = 32 then evaluate (Answer accurate to two decimal…

A: Given:We are required to find:

Q: gallons, 12,000 gallons, and 24,000 gallons. How many of each type of tank car should be leased? Let…

A: Let x1 be the number of cars with a 6000 gallons capacityx2 =The number of cars with a 12000 gallon…

Q: How would you express the equation of a sphere with a center at the origin (0, 0, 0) and a radius of…

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Q: A slice of a circular pizza 10 inches in diameter is cut into a wedge with a 90° angle. Find the…

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Q: Compute the surface area of the solid of revolution formed by rotating the bounded region formed…

A: To compute the surface area of the solid of revolution formed by rotating the bounded region formed…

Q: State the domain for the function: h(x) = -4*-1 O (0,00) O (-∞, -1) (-00, 0) (-00,00) O l

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Q: ii. Consider the following differential equation: d²x dx dt² +5+8x = f(x) where f(x) is the input…

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Q: Question 1 Let 0 = cos¯¹(-³) where 0 ≤ ≤. Find the exact value of 0.

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Q: Using cylindrical shell method, find the volume of the solid S: R is the region bounded by x= y²+1…

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 8.…

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Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

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Q: (8) Find y' using implicit differentiation method: Sin(y) =sin(x) cos(y) + 4

A: To find

Q: Calculate the iterated integral. [²(6x²y- (6x²y - 4x) dy dx

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Q: You will integrate the following rational function: s 4x2-14x-3 (x-9) (x2–2x+2) To do this, start by…

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Q: At which of the five points on the graph in the figure are first and second derivative both…

A: We need to choose the point at which both 1st and 2nd derivative is positive.

Q: 2. Sketch the line = (-4,-4) + t(6,8).

A: To sketch the line r=(-4,-4)+t(6,8)

Q: 3. Find the equation of the line or plane ( c) The line that is perpendicular to the line 2x-3y +1=0…

A: Find The Equation of the Line or Plane :c.) The line that is perpendicular to the line 2x – 3y + 1 =…

Q: (cos x - xsinx)ydy + (x cos x - 2y) dy = 0

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Q: x + 3y¯−¹ = 1/2 x (5) Find y' be implicit differentiation: +

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Q: You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person,…

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Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Region bounded by x-axis and Using Disk method , Volume of solid of revolution about x-axis will be

Q: Calculate the area, in square units, bounded by g(x) = 4x + 8 and f(x) = x² + 19x+62 over the…

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Q: lim t→0 4t² + 3t sin t +2

A: To evaluate the following limit.

Q: Which of the following ideas represent the different ways a line and a plane can intersect. Select…

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Q: Consider the region bounded by the graphs of y = x², y = 30, and x = 11 in the first quadrant. What…

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Q: {(1,5), (-2,3)} is a spanning set for R². Express the vector (4, -3) as a linear combination of the…

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Q: Find the integral. 2 sinx S x dx

A: As per the Bartleby guidelines, answering only first question as the other question is not the sub…

Q: 5. A certain computer that is purchased today depreciates in value according to the function (t) = =…

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Q: Consider the function f(x) = (a) Find the domain of f(x). Note: Use the letter U for union. To enter…

A: Note : as our guidelines , we  can solve first three subparts . Please repost remaining parts or…

Q: Explain why the following justification is incorrect: To evaluate the limit of the function x² + y²…

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Q: Evaluate the following: We need to calculate the limit of the function f(x, y) as (x, y) approaches…

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Q: Suppose the line tangent to the graph of f at x = 4 is y=6x + 1 and suppose y=2x-3 is the line…

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Q: 29. Find the equation of the tangent to the curve y = 4x-tanx at the point where x = 품.

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Q: Find the arc length of the curve x = − Length = ▶ —4y³/² from y = 0 to y = 2.

A: Given here the arc length of the curve  in the interval  from

Q: The region is bounded by the curves

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Q: 3e4x-2e-4x lim x-∞o 5e4x+e-4x X-8

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Q: Let ā = ( – 5, — 4, 5) and - 4, 5) Find the projection proja b 6 and 7 = (3, 1, 0). =< of b onto a.…

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