Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

Q: Let u(t) = 4t³i + (t² − 1 )j – 3k and v(t) = e¹i+ 9e¯¹j- et k. Compute the derivative of the…

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Q: Please calculate whether this function is also differentiable, as well as continuous. Thanks.

A: Continuity at x=a:Differentiability at x=a:

Q: Find the gradient field of the function, f(x,y,z) = (3x² + 2y² + z²) −1/².

A: According to Bartleby Guidelines, we can solve only first question from multiple question, please…

Q: Find the slope of the curve below at the given points. Sketch the curve along with its tangent lines…

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Q: 2. Find the indefinite integrals. (You may want to differentiate to check, but it's not required) a)…

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Q: Question Given the price-demand and price-supply equations below, determine the equilibrium price…

A: The objective of the question is to find the equilibrium price and the producers' surplus using the…

Q: Use Newton's method to estimate the one real solution of x³ +5x-4 = 0. Start with x = 0 and then…

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Q: Considering the definition of f(x) below, find lim f(x). x-*6 Select the correct answer below: O -56…

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Q: Express your answer as a polynomial in standard form. f(x) = 2x² - 4x - 6 g(x) = 2x + 7 Find:…

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Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

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Q: A company estimates that the revenue (in dollars) from the sale of x doghouses is given by the…

A: The objective of this question is to find the approximate change in revenue when the sales of…

Q: Let f(x) = x³, and compute the Riemann sum of f over the interval [2, 3], choosing the…

A: The given function is The midpoint rule

Q: Let f(x) = x³, and compute the Riemann sum of f over the interval [6, 7], choosing the…

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Q: For Questions 1 and 2, region R is bounded by f(y)=y²-14 and g(y) = 2y + 1. Which of the following…

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Q: Use the zero, 5+ i, to write P(x) as a product of linear and irreducible quadratic factors.…

A: we need to write P(x) as a product of linear and irreducible quadratic factors

Q: A box with a lid is to be made from a rectangular piece of cardboard 11 cm by 16 cm, as shown in the…

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Q: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

A: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

Q: 2) Find the first derivative given that f(x)= 5x √2x+3

A: we need to find out the first derivative of the given function."As per the rules, we are supposed to…

Q: 6. Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = x²…

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Q: For Question 5, region W is bounded by f(x) = 4+√9-x², g(x) = cos 7 104 9 8 7 6 5 4 3 2 1 + + + -3…

A: Region W is bounded by f(x)=4+9−x2,g(x)=cos⁡(π6x),x=0, and x=3 Area =∫03[f(x)−g(x)]dx

Q: Suppose a dog jumps in the air and that its height (in feet) above the ground is given by h=-16t²…

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Q: 13. y = 5 x², y=3-x. —

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Q: Which of the following would not be a representation of the differentiable function f, where f'(2) =…

A: Consider a differentiable function f, where f'(2)=4

Q: 1 sin y Y (a) sketching the region of integration (b) then by evaluating the resulting double…

A: The given integral is

Q: = · (x² + 2x − 12) (x³ + x² − 12x). If there is more than one answer, enter your answers as a comma…

A: The objective of this question is to find all the zeros of the given function. A zero of a function…

Q: Find the area bounded by y=e,y=e^x and y=e^-x

A: Given that the region bounded by the curves

Q: If f'(x) = 5x4, what is f(x)? (Remember the constant of integration.) f(x) =

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Q: Evaluate x dS, where S is the part of S the plane 2x+y+z=4 in the first octant.

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Q: Use the alternative curvature formula k = following parameterized curve. r(t) = (4 + 2t²,2t,0) K=…

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Q: Write the exponential equation as a logarithmic equation. e0.75 = 2.1170...

A: The objective of the question is to convert the given exponential equation into a logarithmic…

Q: Find local extrema f(x) = 4 of the function, if any. x6 - 6x² A. There is no local extremum. B. f(0)…

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Q: the U.S. postal service will accept a box for domestic shipping onl if the sum of its length and…

A: Let b be length of the box and a be the length of the side of the square.The volume V of the box…

Q: Using the € - d definition of limit, prove that 2x lim x 2 x + 6 1 NI

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Q: a) Find a potential function for the vector field, i.e., find a function ƒ so that F =Vƒ. b) Use the…

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Q: 7 The rate of change of a population with emigration is given by P'(t) = 300 population in millions,…

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Q: Determine which test can be used to show that the series (a) Geometric Series Test (b) p-Series Test…

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Q: NASA launches a rocket at t=0 seconds. Suppose its height, in meters above sea-level, as a function…

A: The height function of the rocket is h=−4.9t2+205t+108 Here the objective is to find the peak of the…

Q: Find the gradient field of the function, g(x,y,z) = e²z - In (2x² + y²). The gradient field is Vg =…

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Q: Find inflection point(s) for f(x), if any. f(x) = 27x - x³ A. f(x) has an inflection point at x = -3…

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Q: Suppose your newspaper is trying to decide between two competing desktop publishing software…

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Q: Suppose the equation 1 300 y = - 2.2 models the height of an arrow where is the horizontal distance…

A: Suppose the equation,  models the height of an arrow where x is the horizontal distance in feet…

Q: a. Find the area of the triangle determined by the points P, Q, and R. b. Find a unit vector…

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Q: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

A: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

Q: 2. Prove the statement lim(10-4x)=- a limit). Show all your work to find and write a formal proof.…

A: Limx-3(10-4x) =-2

Q: 2) Find the derivative of the function f(x)= x arctan(2x) ——In(1+4x²).

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Q: 2x² + 5x = x + 4y

A: 2x2+5x=x+4y

Q: The grid on the right shows the graphs of several functions f(x) whose slope at 8x each x is Find…

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Q: The graphs off and f' are shown over the domain [-8, 1]. m Graph of f Graph of f' Part A: Calculate…

A: The given graphs f and f' are shown the domain (-8,1)

Q: Find a parametrization of the line in which the planes x+2y+4z=-4 and 2x+3y+6z= -7 intersect. Find…

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Q: Select the graph for which f(x) > 0 and a) r f(x) < 0

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