Determine whether the given set of functions is linearly independent on the interval (-∞o, ∞o). f₁(x) = 6, f₂(x) = cos(x), f(x) = sin²(x) O linearly dependent O linearly independent

Q: 1. DIFFERENTIAL EQUATION (2y³ + 4) dx = (6-2xy²) dy

A: Note :- These are multuple questions and according to our comapny guideline we can do maximum 1…

Q: Solve the initial value problem: y(x) = 2x - 4y√x² + 1. dy dx = 0, y(0) = -4

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Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: - The complementary function is १ex . Ус where C₁, C₂, C3, C4 си the particular Solution se = c₁ex +…

A: This is a problem of ODE. Please follow the procedure given below.

Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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Q: Find the EXACT solution to the equation below (do not give a decimal approximation; the logarithm is…

A: NOTE: Refresh your page if you can't see any equations. . properties of logarithms are

Q: 1) y" - 36y = 0.

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Q: the particular Solution is 1 84-1 2. = 2. 1 04-1 — (ex) - 1/₂₁ (2x), D4-1 = LYDB (ex) = 4p3 De_…

A: Given D4-1y=2 sinhx+sinx The auxiliary equation is m4-1=0⇒m22-12=0⇒m2-1(m2+1)=0 Therefore m= ±1, ±i…

Q: Tutorial Exercise Find the domain of the function. 7 |x²-161 g(x) = Step 1 The domain is the set of…

A: To solve the given domain problem of the functions.

Q: The approximate rate of change in the number (in billions) of monthly text messages is given by the…

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Q: f(x) =  5 x2 + 6 Describe the interval(s) on which the function is continuous. (Enter your answer…

A: Polynomial function are continuous every where so using this we solve this problem

Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19,2 € + 60e, y(a) = Y(u). 4X -4X…

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Q: tan12/1-tan^2 12 simplify

A: Simplify tan121-tan212

Q: Identify any holes in the graph off(x)= x=-=/ b. x=- x=-- a. 17 X+7 7x +49 C. x=7 d. x=-7

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Q: WHAT IS O H|5 Se-5x dx 1 e -5x + C -e e-5x + C -¹e-5x + C 5 e-5x + C

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Q: The graph below is the function f(x) -5 -4 -3 -2 -1 n 4- 3 I 2 25 N -1 -2 -3 -4 74 ON 12 Select all…

A: Graph of the function is given, we have to find the limit and continuous at x=2

Q: What is the original price of P1,743,759 discounted price at 22% discount?  (whole number)

A: discounted price = 1,743,759  discount rate = 22%  find original price = ?  this discounted price is…

Q: The dose-response curve for x grams of a drug is f(x) = 8(x − 1)³ + 8 for x ≥ 0. (a) Make sign…

A: The solution is given below

Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: 12 f(x) = x² - 6x² + 2 Determine the intervals on which f(x) is increasing/decreasing and identify…

A: Given,  f(x)=x125-6x25+2

Q: A circle starts out with a radius of 1cm. (at time t = 0) and begins growing. The area of the circle…

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Q: Find az/ax if - z = x² sin(xy³) O x³y4 cos (yx³) + 4y³ sin(x³) O x³y³ cos (xy³) + 4x³ sin(xy³) x4y³…

A: Find the derivative

Q: Replacement Time An outboard motor has an initial price of $2,160. A service contract costs $400 for…

A: Topic:- application of derivatives

Q: all company of science writers found that its rate of profit (in thousands of dollars) after t years…

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Q: How did you get 6?

A: For a horizontal asymptote to exist for a rational function, the numerator has to be of the same…

Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x-intercepts…

A: We need to write an equation for a rational function with : Vertical asymptotes at x=-4 and x=2…

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (3, 2, 5)…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: 1. 9x2 + 4y2 = 36 2.222² 쫑 = 1

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Q: Answer without referring back to the text. Fill in the blank. The only solution of the initial-value…

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Q: A force of 660 newtons stretches a spring 3 meters. A mass of 55 kilograms is attached to the end of…

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Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Find all solutions of the equation 4 cos(3θ + π/4)+2=0 in the interval [0,2π].

A: Solution of given question is written in below steps.

Q: 2 Solve the following ODES by Inverse Operator method. (D²³+1) y = 3+²+52x Ans: y = c₁e²+ ¹² (C₂…

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Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: Write an equation for the function graphed below 5+ 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 y = -5+ 1…

A: topic- graph of a function

Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) =

A: Given y''+y=csc(x) Complementary solution: We will solve this equation by variation of parameters…

Q: By power Series method, Solve the following ODES • (2+x)y=y ans: y = a. (1+1=1/2 X

A: In this question we have to find the solution of the power series.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: (b) Identify (3) and g(3). f(3) = g(3)= (c) For what value(s) of x is f(x) = g(x)? x= (d) Estimate…

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Q: 3. A science project studying catapults sent a projectile into the air with an initial velocity of…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Precalculus You have 5% and 20% but need to create 10% solution of 1,000 miligrams . How many…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 6x x-axis…

A: We will find the slope

Q: 18/17-16-15 2 2 1 -13-12-11-18-9-8-7-6 -5 -4 -3 -2 -2 + -2 $ 6 8 9 10 The curve above is the graph…

A: topic- trigonometric functions

Q: is 2 Sinh xt sinh (۱) Let y emx (to) be the trial solution to the Corresponding homogeneous equation…

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Q: Analyze the following graph of f'(x). Select all of the intervals over which f(x) is concave down.…

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Q: The function is not one-to-one. Delete part of the domain so that the function that remains is…

A: Here we have to find the inverse function.

Q: Give the order and degree of the following differential equations. Differential Equation 2 (d²y) dy…

A: Answer and explanation is given below...