Find the equation of a plane that is perpendicular to the vector 57- 2j+ kand passing through the point (-1, -2, 3). The plane is given by:

Q: 4 + 9x ≤ f(x) ≤ 12 + x²

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Q: 1. For the function y = 5x³ - 4x a. Determine the average rate of change between x₁ = 3 and x₂ = 5.…

A: For the function y=5x3-4xa To determine the avarage rate of change between x1=3 and x2=5.b To…

Q: Write the first five terms of the sequence: [11]nn] ¹ n Jn-1 Determine whether the sequence…

A: The given sequence is 11 ln nnn=1∞ we have to find the limit of the sequence.

Q: The measurement of the edge of a cube is measured to be 8 inches, with a possible error of 0.02…

A: The solution is given below

Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: y²dx + x(x + y)dy = 0

A: This question is based on Solution of Homogeneous Differential equation.

Q: Slope of tangent line F(x)= 3x+8

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Q: Given f (x) below, select ALL of the true statements. lim-4+ f (x) = 1 lim, 4 f (x) = 1 lim,-4-f(x)…

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Q: The price-demand equation for hamburgers at a fast food restaurant is given by the equation below.…

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Q: Let ?(?)=4?2−4?−4.f(x)=4x2−4x−4. The secant line through (2,?(2))(2,f(2)) and…

A: To find out the slope of the secant line and also slope of the tangent line at the values given.

Q: Parabola y² = –12x FIND THE: Opening - Vertex - Focus - Directrix - Axis of Symmetry - Latus Rectum…

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Q: Determine the degree of the differential equati 3/2 2/3 (3x² ² 2 + 4xy) ¹ ² = (2y³d² - 4xy)" d²y dx²…

A: The given differential equation is; (3x2d2y/dx2 +4xy)3/2=(2y3d3y/dx3-4xy)2/3

Q: 6. Find the exact value of the distance of between the line passing through (1, 3, 2) and (4, 0, 4)…

A: The objective is to find the exact value of the distance between the line passing through 1,3,2 and…

Q: Find the derivative of the function. 2(5x² + 6x) 73√√x y' = y =

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Q: Find the limit. NOTE: Enter an exact limit if it exists. If the limit does not exist, indicate that…

A: Let's find limit of given function.

Q: , what is the dependent variable?

A: Dependent variable: When an independent variable is changed, the dependent variable's value changes.…

Q: Consider the following graph of the function g. गोरग -2 0 1 2 -3 + N + - M 3 From the given graph of…

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Q: ood to go Evaluate the integrals S√4x²dx 2. S 1 (4+x²)² dx

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Q: ← If √7-6x² ≤ f(x) ≤ √7-x² for -1 ≤x≤ 1, find lim f(x). x->0 lim f(x) = x-0 (Type an exact answer,…

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Q: Y X arb 1.5 Lab Activity In BMX dirt bike racing, jumping high (or "getting air") depends on many…

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Q: A small business can produce a maximum of 54 of its product per month and sell them for $ each. The…

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Q: Evaluate the integral. (Use C for the constant of integration.)       x2 + 4x + 1 (x2 + 1)2 dx

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Q: show that the lim DNE. lim (x, y)→(0,1) In (x4 + 2y² 1) e 2x² + y² - 2

A: Please see the below picture for detailed solution.

Q: Use the vertical line test to determine whether or not the graph is a graph in which y is a function…

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Q: 1- y²dx + √√√1-x²dy

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Q: 4. The function f(x)=x²-x² - 2x + 1 has three zeros on the real line. For each of these zeros, find…

A: We have to locate all 3 real roots of f(x) = x3-x2-2x+1 on the real axis. Given f(x) is continuous…

Q: Let f(x,y)=√√9-x²-3y² State the domain off and sketch it in the x-y plane. The domain must be…

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Q: Find the limit of the following:  a) lim x→∞ (1 - x2 / x3 - x + 1) b) lim x→∞ (x - x√x / 2x3/2 +…

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Q: 5. Use derivative rules to find the derivative of h(a)=3f(x) - 2g(x) - ² f(x) + Show steps fo 6.…

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Q: Evaluate the curvature of r(t) at the point t = 4. r(t) = (3 - 5t, e³¹-12, 8t - t²) (Use symbolic…

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Q: (a) When he is 3 meters from the base of the light, at what rate is the tip of his shadow moving?…

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ?

A: A detailed solution is given below.

Q: Match the graph of f with the correct sign chart. Choose the correct sign chart below. OA. f(x) +…

A: Topic- functions we are given graph of a function ,we need to determine the size chart of f'(x)…

Q: Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the…

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Q: For the function f(x) = 3ˣ find f(x+1)/f(x-2)

A: Topic = Function

Q: Find the differential dy of the given function. (Use "dx" for dx.) 6 √x dy = y = 9√x +

A: Solution is given below:

Q: 4. [secx tan x cos(secx) dx

A: A detailed solution is given below.

Q: 2) The profit (in dollars) of a company is given by P(x) = 840x75.6-0.4x², were x represents the…

A: The given profit function is: P(x)=840x-75.6-0.4x2

Q: Which of the following is true about the differential equation of the family of unit hyperbola…

A: First we will find the differential equation of the family of unit hyperbolacenter at the line y=x.

Q: Which of the equation: Show your A. following is the general solution of the differential X ady - y…

A: The given differential equation is; x3dy - y(x2-y2)dx=0

Q: Find all solutions u of x u =. Show all steps.

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

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Q: Jse any of these formula (an = 1/2 (a₁ + an ) or an = 1/2 [2a₁ + (n − 1)d] to solve for the sum of…

A: As per the guidelines I am supposed to do the first question among multiple questions, So here I am…

Q: Evaluate each limit, if it exists: a)lim ²-4 x-2 X-2 1-x² b)lim x-1 1-x x²-4x x=0 x(x-1) c) lim

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Q: The price-demand equation and the cost function for the production of table saws are given,…

A: The solution is given below

Q: 7. Use Midpoint approximation with n = 6 equal subintervals to approximate the following. 1 ln(x…

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Q: 78. Show that the following limit does not exist: xy³ lim (x,y) (0,0) (3x² + 2y³)²

A: Lim(x,y)-(0,0)xy3/(3x2+2y3)2.

Q: A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine…

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Q: Given the function f(x):  f(x)= x^2 + 1 , − 1 ≤ x < 0          2x− 1 , 0 < x < 1          1 , x = 1…

A: Given the function f(x): f(x)= x^2 + 1 , − 1 ≤ x &lt; 0         2x− 1 , 0 &lt; x &lt; 1         1 ,…

Q: in step one is it f(n) or f(x) i cant tell your hand writing

A: To write down that it is f(x) or f(n).