Discover the standard equation for the plane that passes through the points P(1, 2, 2), Q(2, 1, 2), and R(3, 1, 1). show your work clearly.

Q: f(x) = 4 X geº.

A: f(x)=4x−9ex

Q: How close does the line y = 6 + 2x come to origin? The closest distance the line y = 6 + 2x comes to…

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Q: (a) Use the Ratio Test to verify that the series converges. lim n! n (b) Use a graphing utility to…

A: The given series to be analysed is,, so, we get the n th term, .(a)Now, the ratio test is as…

Q: Solve the given linear system using Cramer's rule. [4 21 (31-0 15 31

A: given system of equation

Q: The graph of the function g on the closed interval [0, 9] consists of four line segments, as shown…

A: The graph of the function g is shown as,Let,f be the function defined by

Q: A given poll states "61% of high school graduates felt they were prepared for college." If there is…

A: The objective of this question is to calculate the 95% confidence interval for the given statistic,…

Q: Find each derivative. Do not type any spaces. dr [10x²] [7] = d-8a] = [-5x² +14x - 9

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Q: Sketch the region enclosed by y=7x and y=8x2. Find the area of the region.

A: The objective of this question is to find the area of the region enclosed by the curves y=7x and…

Q: please utilise implicit differentiation to calculate dy/dx if you are given:  a) (x^2)+(y^2)+xy=3…

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Q: Find the area of the surface over the given region. Use a computer algebra system to verify your…

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Q: If f(x)=x²-10, find an equation of the tangent to the curve passing through the point (5, 1). A. y-1…

A: Given,.Given point is (5,1).

Q: The functions f and g are differentiable and have the values shown in the table. If A = f + g, then…

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Q: Question 4.2. In each case let R be the region under f over the given interval and let S be the…

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Q: A B C D 6 13 The table above gives the values of the differentiable functions f and g and their…

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Q: 2. y" + xy = 0; y'(0) = 0, y' (π) = 0

A: As per our company guidelines we are supposed to solve the first question only. Please repost other

Q: Dengue-fever viruses are carried by mosquitoes. There are several different serotypes of the dengue…

A: From the given statement

Q: Let g be the function given by g(x) = x² - 2x³ - 3x. What are all values of a such that g′ (x) =…

A: The given equation of function

Q: The temperature at point (x, y, z) on the sphere x² + y² + z² = 4 is given by T(x, y, z) = 100xyz².…

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Q: 9 Consider the function f(x) = 6x⁹ + 6x7 - 7x² - 4. Enter an antiderivative of f (x). Do not enter…

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Q: Given: (x is number of items) Demand function: d(x) = 396.9 -0.4x² Supply function: 8(x) = 0.5x²

A: Demand function: d(x)=396.9−0.4x2Supply function: s(x)=0.5x2

Q: True or False? The function f (x,y) = x2 + y2 has a global minimum on the disc x2 + y2 < 4.

A: The objective of the question is to determine whether the function f (x,y) = x^2 + y^2 has a global…

Q: The piecewise function f(x) is graphed below. Use geometric formulas to evaluate the following…

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Q: Find c such that f'(c) = 0 and determine whether f(x) has a local extremum at x = c. f(x) = e¯x²…

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Q: Below is an attempt to derive the derivative of csc a using the product rule, where x is in the…

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Q: 21. f(x) = 2 cos³x + 3 cos x, 0≤x≤π.

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Q: 10-01- does not exist. 5. Use the two-path test to prove that lim xy (x,y) →(0,0) x² + y²

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Q: The figure below shows the graph of f. Use the figure to answer lim f is x--6+* A. 1 D. no limit 22…

A: We have to find the limit of piecewise function from the given graph

Q: Which of the following is an antiderivative of f (x) = tan (e²+ ) on 0 ≤ x ≤ ln ( 7 ) ? A B D sec²…

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Q: 3x - 6 Given a function is defined by f(x) = x² + 3x- 10 for what value(s) of x does the function…

A: f(x)=3x−6x2+3x−10

Q: Assume f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 3 f(x) g(x)* Find h'(3) given h(x) = A. -2 B. 2/2…

A: Given,

Q: C(x) 1 Suppose that the total cost (in dollars) for a product is given by 1400 + 190 ln(2x + 1)…

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Q: A differentiable function f is given by the table. Estimate f'(4.3): X f(x) 3.7 4.3 4.9 5.5 6.1 1.8…

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Q: Consider f(x) = (x + c cx² +5 for x < 3, for x ≥ 3 For what value of the constant c is f continuous…

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Q: *A company manufactures coffee makers and has total revenue function R(x) = 39x -0.01x² where is the…

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Q: 5. The graph of y = f(x) is shown below. The sketches of transformations of f(x) are given in the…

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Q: 16 / FLX Evaluate 1+√3 2 f(x, y, z) ds. f(x, y) = 3y - X S: r(u, v) = cos(u)i + sin(u)j + vk 0 ≤us π…

A: We have to evaluate the integral.

Q: I need a clear explanation about the radius function of the volume shell. In part a, the radius…

A: Note:-As per your demand we solve part a and b for radius of region.Given that the region is bounded…

Q: Show that I is not a zero of 3 2 P(x) = 8x³ + 6x² – 3x-1 -

A: To show that  is not a zero of the following polynomial.

Q: Using only power series techniques and algebra, evaluate the following limit. lim      ( 1-e^ax) /…

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Q: Given the point (3,-2) is on the graph of z=f(y), determine what those coordinates would be on the…

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Q: So Find the EXACT answer, then round it to THREE decimals. Evaluate the improper integral: 1 4+x² dx

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Q: 21. Set up but don't evaluate the triple integral for finding the volume of the wedge bounded by the…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

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Q: Most medical tests are not completely accurate. For example, a microscopy test for tuberculosis…

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Q: Let f be the function given by f (x) x³ − 6x² + p, where p is an arbitrary constant. Write an…

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Q: v(t) = t³ - 5t² + 6t; 0 ≤ t ≤ 5

A: The given velocity function is  ,

Q: Evaluate 1dx using Simpson's rule with N = 4 1+x3

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Q: [1 Find the inverse of the matrix C = 0 12 operations. Show all your work. 0 1] 1 1 4. 1 using row

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Q: Let f be defined as follows: x²-16 x-4 for x # 4, for x = 4 Which of the following are true about f?…

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