Suppose that f(x, y) = 3x²y² + 9x² + 7y² then find the discriminant of f.

Q: Evaluate the definite integral. 1 lis 0 (5* −_4*) dx

A: solution:-∫015x-4xdx=∫01exln5-exln4dx=exln5ln5-exln4ln401=e1ln5ln5-e1ln4ln4-e0ln5ln5-e0ln4ln4=5ln5-4…

Q: [(5x²³ -2.r²+3)dx

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Q: A farmer finds that if she plants 100 trees per acre, each tree will yield 45 bushels of fruit. She…

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Q: Find the points on the curve y = x³ + 3x² - 9x + 9 where the tangent is horizontal. (x, y) = smaller…

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Q: 9 Find the with a area of the parallelogram Verticles vertices; PC0,0,0), QC3₁=3₁-9), R (3₁-1₁-²5)…

A: I am attaching image so that you understand each and every step.

Q: A homogeneous function is one such that f(tx, ty) = ta f(x, y) for some a. (a) Show that f(x, y) =…

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Q: O-11 60

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Q: 2. Find the curvature to the vector-valued function r(t) = (sin(t), cos(t), t²) at t = 4.

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Q: x² 421875 For the given cost function C(x) = 54√√x + a) The cost at the production level 1700 b) The…

A: Note:- These are multiple sub parts but we can solve max 3 sub parts so i am solving here first 3…

Q: Given y = f(u) and u = g(x), find (1) × ² y=9u-2,u= dy dx = f(g(x))g'(x).

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Q: Find the area of the region inside the circle r = 36 sin and outside the cardioid r= 12 + 12 sin 0.…

A: Concept: The area between the circle r1 and the cardioid r2 is A=12∫θ1θ2r12-r22dθ Here θ1 , θ2 are…

Q: Find the tangent, unit tangent, and unit normal vectors for the curve r(t) = (2t²+1, 2 sin(t),…

A: Given that, r(t)=<2t2+1,2sin(t),ln(cos(t))>We need to find tangent, unit tangent and unit…

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The objective of the question is determine the gradient at  a point and directional derivative at a…

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.01q² + 6q - 46, where q…

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Q: Question Determine the interval of convergence for the power series that can be used to represent…

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Q: 112 15 A rocket is being launched. After a while, it rises at a constant velocity of 10 miles per…

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Q: Write the function below in the form y = f(u) and u = g(x), then find y = cos (csc x) What are the…

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Q: nd a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = surface y =…

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Q: Use the graph to locate the absolute extrema (if they exist) of the function on the given interval.…

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Q: Exercise 1. Let an 2n 3n+ 1 (a) Determine whether (an) is convergent. (b) Determine whether an is…

A: Part (a) A sequence an is said to be convergent if limn→∞an exists and is finite. Determine limn→∞an…

Q: 3 [(1 + 5a)'di

A: Solve the integral

Q: If demand is unitary when the unit price is p = $7, then revenue will decrease if the unit price is…

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Q: Determine the value of an investment in the amount of $4000 that matures in 4 years and pays 7.5%…

A: Let's find value of amount after 4 years in each given cases.

Q: 4. Find the area bounded between the two curves y = 5x² - 2x and y = x³ - 5x+3. (You may use Desmos…

A: To find the area bounded between the two curves y=5x2-2x, and, y=x3-5x+3.

Q: > Read over Example 4 carefully. Then show how you decompose the following rational expression into…

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Q: what is the set of whole numbers, positive integers, negative rational numbers, and natural numbers?

A: To write: The set of whole numbers, positive integers, negative rational numbers, and natural…

Q: lim x3 x²+2x+3 x+3

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

Q: Find the indefinite integral. (Use C for the constant of integration 2 cosh(√x) X dx

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Q: Find the absolute maximum and absolute minimum of the function f(x) = 3 sin (x) cos (x) over the…

A: We will find the required.

Q: f-¹(x) = The domain of f-1(x) is all x f(x) = 6x - 12 13x + 9 be careful with your parentheses in…

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Q: Find x. Round your answer to the nearest tenth of a degree. 44 X 24 -0° x =

A: We have given a right angle triangle  From given triangle  Perpendicular (p) = 44 Base(b) = 24 Using…

Q: +In+siny) dy = 0 xcos (xy) + 2y] dy 1. (e+ Iny +) dx + 2. [e²y ycos (xy)] dx + [2x²y 3. (10-6y+e-3)…

A: Since you have posted multiple questions, as per guidelines we are supposed to answer only first…

Q: Find 7' (t), given r(t) = (- 4√t, - 3 ln(3t), 3e-³). F' (t) =

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Q: Find the derivative of the function below. h(x) = x tan (8/x) + 1 dh

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Q: 6x Find the derivative of h(x) = 2 h'(x) = 36log, (x) 6

A: Topic:- application of derivatives

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: Solve the right triangle. Round your answers to the nearest tenth. 50° 26 B B = ₁ -0 c = 0 a = X

A: We can find the required answers using the given right triangle in the below steps.

Q: 3. The slope of a curve at the point (x, y) is given by 3x²y + 2y. Find the equation of this curve…

A: To find the equation of the curve with given slope

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: Rewrite the equation of the line 2x+3y=6 from standard form to slope-intercept form

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Q: f(x) is concave down on the interval (a, b) if f'(x) is decreasing on True False (a, b).

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Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

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Q: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.) 6 1 -…

A: Let's convert given polar equation to rectangular coordinates.

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (-3, -4) and the direction in…

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = 7 sin(y), osys. 1. (C dy 2

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Q: Find an equation of the tangent line to the graph of the function at the point (-1, 4). y = 4 x y =

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Q: Let dy dx V 2 + by = ay + . Find at (2, 0). O 73 23 13 | من 0 19 3 ان | دن 3

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Q: First the pieces: 25 5353 7 23 SS 8z as by And putting it all together: dz dz dy dr Ot dy Ot

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Q: Find the following using the table below. 1 2 3 4 1 3 2 4 4 2 f(x) f'(x) 13 g(x) 23 14 g'(x) 1 2 4 3…

A: Explanation of the answer is as follows