Suppose a triangle in space has vertices (a, b₁, ²₁), (a₂, bz, C₂) and (93, b3; (3). Explain how you find a vector that is perpendicular to this triangle. Use the vertices to guide us through your process. ر at Points

Q: Consider the function f(x) = 4x²e-. a. Find the first derivative. f'(x) = b. List any critical…

A: According to our bartleby expert guidelines only first three subparts are to be answered kindly…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4+x² - y2…

A: The given function  and region R

Q: 7. Σ n=2W 3 2 n2 + I 00 8. Σ n?e=n n=1

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Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: Find the total differential. 8x + y 3z - 2y dw = W X

A: If W = f(x,y,z) then the total differential of W is given by   +

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 2xe…

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Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

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Q: For what values of a and b does lim x→0 a = b = sin (2x) x³ +a+ b 2/2) = x² = 0?

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Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

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Q: Consider the equation below. f(x) = 4x³ + 9x² - 54x + 1 (a) Find the intervals on which f is…

A: In this question, we will find the interval of increasing and decreasing.

Q: Evaluate the following integral using integration by parts. Se 10x cos x dx

A: I=∫e10xcos⁡xdx

Q: Consider the following. f(x) = √√49 - x² Find the critical numbers. (Enter your answers as a…

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Q: Let f(x) = 2x + 3 and g(x) = -3x - 6. Compute the following. (a) (fog)(x) (b) (fog)(9) (c) (gof)(x)…

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Q: Use a linear approximation (or differentials) to estimate the given number sqrt(99.2)

A: SolutionLet f(x)=√x and use the linearization at a=100

Q: Labor. Refer to Table 4. (A) Find the average rate of change of weekly hours from 1980 to 1990.…

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Q: For the functions f(x)=x^2-6x+10 and g(x)=5, determine the following information. Vertex of…

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: find maximum rate of change of f(x,y)=x sin(y) @ the point (2,0)

A: To find the maximum rate of change of at the point .

Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: b.Let f(x)=x²-3x² -1, x ≥ 2. Find the value of af dx at x = -1.

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Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. maximum value:…

A: To find the maximum and minimum values of f(x,y)=xy on the ellipse 5x^2+y^2=4, you can use the…

Q: Suppose that lim ƒ(x) = 0, lim g(x) = 0, lim h(x) = 1, limp(x) = ∞, and x→a x→a x→a x→a lim q(x) =…

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Q: Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the…

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Q: Consider the following situation. A company purchased computers for each employee and two all-in-…

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Q: A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see…

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Q: Find a formula for the nth term of the sequence where an is calculated directly from the value of n.…

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Q: List the first five terms of the sequence. an 1 + an a1 a2 аз a4 a5 || = = = a₁ = 6₁ an+1 =

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Q: 2. Consider 1, 0.1, 0.01, 0.001, 0.0001, ... (a) Write out the next three terms of this sequence.…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Assume that  are both  differentiable  functions of t.(a) To find , given that (b)  To find , given…

Q: 5 Determine the difference quotient for the function f(x) = 2x-1.

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Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

A: Radius = 60cmdr/dt = 0.01 cm/min.

Q: Solve dy/dx = y2 - 4

A: Given the differential equations we have to find solve the equation

Q: Solve the second order. 1. eq Y Ý + Y

A: The given differential equation is

Q: Write an equation for a line perpendicular to y y 4-4 and passing through the point (-8,7)

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Q: Let f(x) = 5 − 3x²2 and g(x) = x + 5. Compute the following. (a) (fog)(x) (b) (c) (e) (fog)(-1)…

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Q: Let f (x) = - x² – 3. Find and simplify ƒ' (x) and ƒ" (x). x5 f" f'(x) = A = -3 B C = || f" (x) D E…

A: Given Function f( x ) as follows

Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing.…

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Q: Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 22-2-3 (b)…

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Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: 2. (y +y²)dx - (y²- 2xy+x)dy = 0

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Q: The following data show the number of months patients typically wait on a transplant list before…

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Q: Use the quotient rule to find the derivative of -10 sin(x) - 1 6x² +5 You do not need to simplify…

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Q: X 3. Verify that f(x)=- satisfies the conditions of the Mean Value Theorem on the closed interval…

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