Let f(x, y) = x² - y³ – 18xy List the critical points: The critical point at the origin is a Select an answer The critical point with negative y value is a Select an answer Submit Question

Q: Q8 Compute the following derivatives: (a) [e5x²-7x] d dx (b) [In(x³ - 5x)] dx

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Q: The Laplace transform of f(t) = el-t is equal to L{f(t)} = Select one: O True O False = e 8- 1

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Q: Find the area of the shaded region. -1.0 -0.5 y co 8 6 y=3e* 4 2 0.5 (1, 3e) y=3xe¹² 1.0 1.5 2.0 X

A: The given equation of curves are y=3ex and y=3xex2

Q: X 0 2000 A television camera at ground level is 2000 feet away from the launching pad of a space…

A: The angle of elevation of the camera is given by: θ=tan-1x2000 Using the Pythagorean theorem:…

Q: Use the Quotient Rule OR Product Rule to find the derivative of p(x) exponents. = 1 (2x-5)³. Write…

A: We know that the quotient rules of the derivative is d/dx(u/v) ={v*(du/dx)-u*(dv/dx)}/v^2

Q: use the vectors u= and v= to find the indicated quantity 3u * v= State whether the result is a…

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Q: In each of Problems 8 through 11, use the linearity of the Laplace transform to find the Laplace…

A: Use the linearity of the Laplace transform to find the Laplace transform of the given function; a…

Q: a) Show all steps to convert the parametric curve into Cartesian form: x = 4t, y=t² − 3| b) Identify…

A: The parametric curve equations are x=4t ,y=t2-3

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 5, 2), b = (-1,…

A: a=1,5,2b=-1,1,4c=5,1,3

Q: Question #3 - Find the First Derivative Test to find the relative extrema and the intervals where…

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Q: 60. A certain automobile depreciates according to the formula ... V = 7500 1 + 0.4t+ 0.1t² where t…

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Q: What is the derivative of this problem, and show your solution by using DEFINITION (x+∆x) not…

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Q: (c) 303x + 204y = 6.

A: 303=1×204+99204=2×99+699=16×6+36=2×3Hence gcd(303,204)=3 3 divides 6 so integer solution exist.

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 15 - x, y…

A: To find the volume of the solid obtained by rotating the region enclosed by the  graphs of y=15-x,…

Q: Find the slope of the tangent line to the curve x² + 4xy-y³ = -5 at the point (-2,1).

A: We need to calculate the slope of the tangent line to the curve: x2+4xy-y3=-5 at the point -2, 1.…

Q: The graph off shown below has vertical asymptotes at x = 3 and x = 6. Find the following limits. Use…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the…

Q: Solve the differential equation. dy dx 3.2 3³3x² + y = 2 = + C 3x√√y X for y # 0

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Q: 6) Consider the vector function r(t) = (sin(nt), ln(-t+3), ²) a. Evaluate lim r(t) t-3- b. Find r'…

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Q: Create an equation or problem involving the Slope of a Tangent Line that is equal to 1.

A: Given slope of the tangent line is equals to 1  As we know that slope is denoted by dydx

Q: A plane is travelling S 35° W at an airspeed (speed in still air) of 250 km/h. A wind of 95 km/h is…

A: Given that , Air speed = 250 km/h S35°W Wind speed = 95 km/h SE Determine the resultant ground…

Q: The function f(x) = 2x³ − 42x² + 240x-2 has two critical numbers. The smaller one is x = and the…

A: given function is f(x)=2x3-42x2+240x-2

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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Q: Question #13 Let_ƒ(x,y)=3x²y³ +2x−3y² +5. Find the following...

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Q: Approximate the area under the curve graphed below from x = 2 to x = 6 using a Left Endpoint…

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Q: Q4. The half-life of mass of 500 mg: Plutonium-210 is 140 days. Suppose that a sample of this…

A: The half-life of Plutonium-210 is 140 days. Suppose that a sample of this substance  has a mass of…

Q: Evaluate the definite integral 3 fat- (t-5) (6-t) dt NO

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Q: Let R be the region bounded by the graphs of x=y^2-4 and 1/8 y^4-y^2+2 as shown below. Calculate the…

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Q: Show that F(x) = 4x² + 6x +5 is anti-derivatives of f(x) = 8x + 6

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Q: Use the shell method to find the volume of the solid generated when the region bounded by: y=(1+x²)…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

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Q: Evaluate fxy³dx + x²dy, where C' is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

A: Evaluate ∮xy5dx+x2dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

Q: Evaluate the definite integral. 2 [²8. 8x dx

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Q: Evaluate the integral. 1²(9x² (9x² + 4ex) dx

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Q: Q3 Find the derivative of f(x) = ln x5 (b) = (a) SIX ४ ज (c) = (d) 5ln x4 x

A: Givenf(x)=ln(x5)

Q: 36. f(x) = 2x x-1 y

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Q: Σ016 – 1)"(ne=")

A: Here, we need to determine the convergence or divergence of the series S = Σ ((-1)^n) * (n *…

Q: Determine the derivative in fully factored, simplified form for y = (x + 1)³(2x − 1)².

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Q: 27. The region bounded by y=x ³ the x-axis, the line x = 1, and x = 5. 3 28. The region bounded by…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: In the diagram shown, lal = 6 and || = 10, find each of the following: a. a.b b. b-b c. à x b d. The…

A: We are authorized answer three subparts at a time, so we are answering the first three subparts,…

Q: 2 n+n+1 3″(n+1) n=1² n, 2

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Q: Suppose that a pencil holder is in the shape of a right circular cylinder, which is open at one of…

A: Suppose that a pencil holder is in the shape of a right circular cylinder, which is open at one of…

Q: In Exercises 23-30, find an equation of the tangent line to the graph of f at the indicated point.…

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Q: Evaluate fx sin² x dx.

A: Find integration of x(sinx)^2

Q: Create a problem where the equation of a line that has an absolute max of 5. Please show steps, (it…

A: We need to construct a problem where the equation of a line that has a absolute max of 5.

Q: Create a problem or equation where the average rate of change is 14. Please show steps. (it cannot…

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Q: The figure shows an open box with a square base. The box is to have a volume of 10 cubic feet.…

A: Given volume of box is 10 cubic feet. Volume of box = Length * Width * Height 10 = x * x * y 10 =…

Q: Find the cross product a x b. a = (2, 5, 0), b = (1, 0, 3) Verify that it is orthogonal to both a…

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Q: To enter π, type "pi". Suppose the volume of the solid obtained by rotating the region bounded by…

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Q: The set {xRx-2≥0 or − 3x > 1} can be expressed in interval notation as:

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Q: V3 4 dx (tan¯¹ (x)) (1 + x²)

A: ∫134tan-1x1+x2dx