f₁(x) = 9, f₂(x) = cos²(x), f3(x) = sin²(x) linearly dependent linearly independent

Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

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Q: Find the general solution of the given higher-order differential equation. d'u 분 700분 - 20분 +7. dr5…

A: The given differential equation, d5udr5+7d4udr4-2d3udr3-14d2udr2+dudr+7u=0

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: f(x)=ax^3+bx find the derivative

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Q: Solve the given initial value problem. y" - 4y' + 3y = 0; y(0) = -1, The solution is y(t) = y'(0) =…

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Q: For So √ 1² dt. use a change of variables to evaluate the definite integral. √5+t²

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Q: Use the limit definition of the derivative to calculate the derivative of f f'(x) = f(x)=-3x³ - 2x +…

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Q: 8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

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Q: Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

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Q: Match the differential equations and the description/s that is/ are true to the differential…

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Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

Q: • У -ky = 19.2 2 + воё, усо) =ўс 4Х -ЧХ 4X Ans: Y = 22ë + +24xе X -Че

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Q: A population of rabbits oscillates 29 above and below an average of 75 during the year, hitting the…

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

A: Answer and explanation is given below...

Q: 6) Identify the vertical and horizontal asymptotes of (x)= x-4 - 2x+17 b. vertical-x- 4, horizontal:…

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Q: Graph f, locate all points of discontinuity, and discuss the behavior of f at these points. -1+x if…

A: In this question we have to find which graph is best for the given function.

Q: Suppose that $600 are deposited at the beginning of each quarter for 10 years into an account that…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: A population grows according to an exponential growth model, with Po = 40 and P₁ = 72 - Complete the…

A: topic- exponential function

Q: Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x²…

A: In this question we have to find the gradient of the function. Note: As per our policy we can solve…

Q: Solve the problem. 16) The graph shows the height h (in meters) of a roller coaster t seconds after…

A: In this question, we need to find the time intervals in which the height of roller caster is…

Q: Determine the graph of the equation. -x² - y² =z Choose the correct graph of the equation. O A. at…

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

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Q: at ch Use the Fundamental Theorem to show that the following is true. a f b C b [ f(x) dx = ff(x)dx…

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Q: Solve the following ODES by Undetermined Coeff 11 X 4X y 16 y = 19.2 € + 60 e - , уса) =ўс=0 THY 4X

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

Q: Given that the graph of f(x) passes through the point (4, 2) and that the slope of its tangent line…

A: Recall: The slope of the tangent line to the curve f(x) is f'(x).

Q: A store has determined that the number of Blu-ray movies sold monthly is approximately n(x) =…

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Q: Зу" +y=0.

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Q: 2. Find lim (√x + 2 = √2).

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Q: For k(x) = (x + 1)(2x)(-3x²+2x+3), find the derivative of k(x) at the point x = 0 using the product…

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Q: Find the area between the curves. 1/5 6/5 y=x, y = 4x ... The area between the curves is (Do not…

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Q: Question 4 An artist has decided to finish their piece of artwork by balancing it on a fulcrum and…

A: Given that y=sinπx+4bounded by x=0,x=2 and y=0Solutiuon :centroid x¯…

Q: Given F(x, y, z) = ei + (xe + e*)j + ye² k. (a) Show that F is conservative by finding curl F. (b)…

A: use the fundamental theorem of calculus and partial derivative for finding the line integral.

Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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Q: Find three positive integers x, y, and z that satisfy the given conditions. The sum is 33, and the…

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Q: Write an equation for the function f(x) shown. The leading coefficient is 1.  Asymptotes: y=-1 x=…

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Q: Find the limit as k approaches infinity for k ^(1/k)

A: Topic:- calculus

Q: Write an equation for the function graphed below. The y intercept is at (0,0.3) 5+ 4- 3 5-4-3 1 1 2…

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Q: Using Desmos or other graphing software, sketch the graph of y = sin (2x). a. Using the tangents,…

A: Y=sin(2x)

Q: Evaluate the following definite integral by using suitable trigonometry substitution: √2√3-2² dx.

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Q: Match the following iterns for the integral of (12) Using partial fractions, the above integral has…

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Q: t Let f(x) = 4x4 + 6. (a) Use the limit process to find the slope of the line tangent to the graph…

A: NOTE: Refresh your page if you can't see any equations. . the given value is x=4 the point on…

Q: g(b)= g'(b)= Calculate g(b) and g'(b) where g(x) is the inverse of f(x) - 18, where b=4 248

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Q: For the given differential equation, what is the a) order, b) degree of the differential equation,…

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Q: y'(x) = 49e²7 -46₂2642 де +2.4e4x + 9.6ne 422 -4 HOW DID HE GET THE VALUE INSIDE THE CIRCLE, CAN YOU…

A: We need to find y'(x).

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Question 25 Use the slopes of tangents to determine whether the function f(x) = -6x² + 36x is…

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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: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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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…