Choose the correct answer Find a function f(x, y, z) such that Vf(x, y, z)= F(x, y, z) = (yz, xz, xy) and use it to compute the line integral - dr where C = {x = t³, y = 1 + t², z = (1+t)²,0 st≤ 1}.

Q: Consider the function f(x) - 2x³ + 45x² - 300x + 5. - For this function there are three important…

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Q: Find an equation of the plane. The plane that passes through the point (-1, 2, 1) and contains the…

A: Given planes:- P1:x+y-z=5P2: 3x-y+5z=3

Q: find the second derivative of the function

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: 27. If = xy² 7-2x²yz7-3yz² find curl 7 at the point (1,-1, 1)

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Q: Find the location of the absolute maximum and absolute minimum of the function on the given…

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Q: Find the exact length of the curve. y 1/4x² - 11/12 In(x), = -X 1 ≤ x ≤ 4

A: We will find the curve length as shown below

Q: Find an equation of the tangent plane to the given surface at the specified point. Z = = 4(x - 1)² +…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 3n 201 3n…

A: Use the comparisonn test

Q: Use linear approximation, i.e. the tangent line, to approximate 8.06 as follows. Let f(x)=√x and…

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Q: Given the function f(x) = x³ + 3x² − 45x + 8 over the interval -10 ≤ x ≤ 5, answer the following…

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Q: so there is no solution on that interval?

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) 256 (c)…

A: Topic = Area

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: What is the correct form of the partial fraction decomposition for the following integral? x² +1 √(x…

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Q: 100 [ k 7k+9 k

A: We  apply here root test

Q: intercepts. f(x) = (x + 1)²(x-4)²(z - 6)

A: Topic = Functions

Q: 44. If 5y² + sin(y) = x² then dy dx = ? 2x 10y + cos(y) 10y + cos(y) 2x 10y - cos(y) 2x 2x 10y -…

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Q: Σ(1) A k! μέρος

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Q: (₂x), _UIS L y = 7

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Q: Determine the solution for the following higher-order homogeneous differential equation. Also,…

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Q: Let f(x) = 9x5 - 7x5. (If an answer does not exist, enter DNE.) (a) Find all critical values of…

A: The given function fx=9x6-7x5. We have to find the critical points and increasing and decreasing…

Q: 6х3 + 2х2 +22х X 2х2 +5

A: Divide the leading term of the dividend by the leading term of the divisor

Q: Which of the following integrals is the area between the graph of f(x) and the y-axis from 0 to 6…

A: Note: Since, there is a typing error in "the area between the graph of f(x) and the y-axis" because…

Q: Stark Technologies produces and sells a internet routers per year at $p per internet router. The…

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: QUESTION 15 Interpret the divergence of F(X,Y,Z) = (x2y.yz², zx²) at a point (1.-5,1).

A: The given vector is:F(x,y,z)→=x2y, yz2, zx2

Q: Graph P(x) = x²-3x²x4x+12 (list all steps, TU

A: Use properties of functions

Q: Given the function f(x) = = 9x³101x² + 274x - 56, and knowing one factor is (9x - 2), write f(x) as…

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Q: Div x²-3x + 7 X-2

A: We will use synthetic division to find quotient and remainder.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

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Q: 15 √x +9 Find the average density Pave (in kg/m) of the rod. kg/m The linear density p in a rod 7 m…

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Q: Using calculus, find the equation of the tangent line to the function f(x) = 3 cos x when = 2.2. The…

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Q: 4. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of…

A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: Consider g(y) = - 12y(-7- y) Determine the intervals on which g is concave down. g is concave down…

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Q: C Suppose a company's revenue function is given by R(q) = q³ + 280q² and its cost function is given…

A: Part A) Write the profit function Pq as the given cost function Cq=290+12q subtracted from the given…

Q: Use the given graph to determine the value of the indicated limits. (a) lim f(x) x--3 (b) lim f(x)…

A: Given Graph:-

Q: QUESTION 16 A line integral in two dimensions may be written as F(x, y)dw. What does (i) F(x, y),…

A: We need to tell about the line integrals in 2 dimensions. Line integrals appear as one of 2 kinds As…

Q: 9) Solve the triangle that has sides 4 ft, 5 ft, and 8 ft. Draw a picture of the triangle with the…

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Q: -10 -8 -6 Answer: f(x) = -4 -2 20 16 12 8 4 -4 do -12 -18 2 9 8 10 Submit Answer

A: Given query is to find the function of the graph.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: (b) If the critical value is 4.605 at a significance level of 0.10, can we reject the null…

A: Answer b) In hypothesis testing, there are two ways to determine whether there is enough evidence…

Q: Use the chain rule to find the derivative of 6√10x8 + 8x7 Type your answer without fractional or…

A: Topic- Derivative of a function We are given f(x)=610x8+8x7Formulas used:chain rule:…

Q: Determine which graph is the graph of f(x) if the following are true. f(0) = -5 f'(x) is positive on…

A: Topic- Functions and application of derivatives We are given f(0)=-5 f'(x) is positive on nowhere…

Q: -5 -4 -3 -2 -1 4 3 2 -1 -2 -3 -4 < X < 1 2 3 4 5 The function graphed above is decreasing on the…

A: Here we have to study the graph.

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: The polynomial of degree 5, P(x) has leading coefficient -3, has roots of multiplicity 2 at x = 1…

A: We have to find out

Q: Given 3x²-5y³ = 4x² + y² - 7 find dy dx and d² dx² y at the point

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Q: For a given cylindrical tank, the radius is 7 m and the height is 13 m. The tank is filled to a…

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Q: Differentiate a. Y = y the following 1 x² + x² +1 b. g(u) = √ 24 +√√√3u functions

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