LESSON 16: SOLUTIONS TO HOMOGENOUS LINEAR DE OF ORDER N. 1. Solve the DE a) y"-y'-2y = 0 b) y" - 9y = 0. when x = 0, y = 0, y' = -1

Q: Current Attempt in Progress Incorrect. Find the area under P = 120(0.7)' between t = 0 and 1 = 6.…

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Q: Find the critical numbers of the function a Comma Seperated Center your answers as list, an answer…

A: Consider the function

Q: Let f(x)=x√x+3. Answer the following questions. 1. Find the average slope of the function f on the…

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Q: True or false: If f is a differentiable function, then [ƒ(√)] = d dx f'(x) 2√x

A: To determine whether the following statement is true or false.If  is a differentiable function, then…

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Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

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Q: 1 = Is the area between the graph of f(x) and the x- axis over the interval [1, ∞) finite or in…

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Q: Consider the following. f(t)= t + cos(t), -2π st≤ 2.T (a) Find the interval of increase. (Enter your…

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Q: Consider the following expressions (a) div(gradf) (b) grad(div F) (c) curl(curl F) Classify the…

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Q: Find the maximum and minimum values of the function g(0) = 40 – 9 sin(0) on the interval Minimum…

A: First we find the critical value of the given function and then find the value of function at the…

Q: Evaluate the following definite integral. Jo 0 F|+ ㅠ 4 3 sin x + 2 cos xd

A: The Sum Rule:The Constant Coefficient Rule:, where is the constant.And use the common integrals:

Q: -5 -4 -3 -2 5 4 3 2 -1 -1 1 2 4

A: A graph of the function is given.The aim is to find the values of  for which .

Q: Use Newton's method to estimate the two zeros of the function f(x)=x-x-2. Start with x= -1 for the…

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Q: (3) Let f(x) = √4-2² be a function. For what value of x in the closed interval [0, 2] does the…

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Q: Suppose R is the solid bounded by the plane z = 2x, the surface z = 2, and the planes y = 0 and y =…

A: R is solid bounded by the plane z = 2x, the surface z = x2  and the plane y = 0 and y = 3. Find…

Q: By trial and error, determine the value of log215

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Q: 376. lim 20-0 √1+x-√1-x x

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Q: (9) Given that g(x) = e(-), which of the following must be true on the interval (0, ∞)? (A) f(x) is…

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Q: 15.Suppose a ball is thrown and the height of the ball is given by the function y(t) = -0.8t² + 50t…

A: Given that a ball is thrown and the height of the ball is given by the function, where t is the…

Q: The graph of f(x) is shown (see figure). 6x x² + 1 f(x) (a) Find the following limits. lim f(x)= x →…

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Q: Evaluate the following integral in spherical coordinates. SSS (x² + y² +2²) 9/² dv; D is the unit…

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Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A: Degree = 5 2 is a zero of multiplicity 3−2 is the only other zeroleading coefficient is 3.

Q: Which represents the correct difference quotient for the function f(x)=4x²-3x+2? A B C D f(x+h)-f(x)…

A: Here we have given a function :

Q: Current Attempt in Progress Find the total area between y = 9 - x² and the x-axis for 0 ≤ x ≤ 4.…

A: This is question of application of integrationHere is function is given We have to find area between…

Q: Consider the following vector field. F(x, y, z) = 3yz lnxi + (9x− 5yz)j + xy³z³ k (a) Find the curl…

A: given vector field

Q: The function g(x) is defined by the rule 9(x)=f(3x+1). If the point (-8, 6) is on the graph of the…

A: We are given that g(x)=And the point (–8,6) lies on the graph of the function f(x).We are to find…

Q: b g(b) Use the Substitution Formula, f(g(x)).g'(x) dx = [f(g(x)) +g'(x) dx = [ g(a) a 1 -1/²/313…

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Q: (8) Find the differential for the function using logarithmic differentiation. y = (sin x) (sec): dy…

A: The given function is .The aim is to find the differential for the given function.Formula used:

Q: The height (feet) of an object moving vertically is given by s= - 16t² + 48t+ 36, where t is in…

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Q: The function f has continuous second derivatives, and a critical point at (-5, 1). Suppose fez(-5,…

A: Conditions are given as follows

Q: Substitution in the Definite Integral S Suppose we want to evaluate the definite integral, H -6…

A: ∫3 5 (- 6) / (9x + 6) 2 dxWe make the substitution u = 9x + 6 As beforedu = (du/dx) dxAnd so, with u…

Q: Evaluate the integral: 1. √64 x² 14x² x = 64 tan(0) 64 sec (0) x = 8 sec (0) x = 8 sin(0) x = 64…

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Q: 1. y'(t) − y(t) = 1, Ans. y(t) = e' - 1 y(0) = 0

A: given IVP

Q: The pollution level near a dump site has been modeled by the equation P(t) = 0.05 +0.12e0.32t, where…

A: Given,

Q: Reverse the ร fit 4 O √5x sle should order dy be of integration 18 doc dy for

A: To reverse the order of the following integration.

Q: Consider the differential equation (4D² + 4D + 1)y = xe-x/2 sinx the associated homogeneous equation…

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given: Length of wire for electric fencing is 2400m, and one side of plot is bounded by a river.

Q: i would like to know how to calculate this without a calculator or big numbers

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Q: find all possible functions with the given derivatives  y'=7x6+9

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Q: Use Green's Theorem to evaluate the following integral, f (et² +24y³3) dx + (2y² - 24x³) dy where C…

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Q: Finish solving the triangle: A ZA = ZB= ZC = 1. a a = C 7 b= 10 C = 9 Enter your answer as a decimal…

A: Consider the triangle

Q: dz əz Find the values of and at the given point. əx dy z³ - xy + 4yz+y³ - 1 = 0, (5,1,1) əz ax…

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Q: Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit…

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Q: For the function f(x, y) = x^2 + kxy + y^2 where k is a constant, determine if f(x, y) has any…

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Q: Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. f(x)=x²-12x+4…

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Q: For Exercises below, solve for the angle 0, where 0 ≤ 0 ≤ 2π. 38. sin² 0 = =1/44 39. sin 20 cos 0 =…

A: we need to solve the given questions and find the solution angle

Q: Suppose we wish to represent the volume of the solid blob B depicted below with a triple integral. 근…

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Q: A stone is thrown from the top of the building. It's height (in feet) above the ground after t…

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Q: Given: (x is number of items) Demand function: d(x) 4624 √x Supply function: s(x) = 4√x = Find the…

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Q: Riemann Sums and Ecosystem Services Definitions: Watershed: the area that drains into a stream,…

A: The objective of this question is to calculate the area under the graph for each watershed to…