Use the properties of logarithms to evaluate the following expression log3(405) - log3(5) 3 81 A 12

Q: Given the initial condition y(0) = 2, find the particular solution of the equation e'y' - 2x = 0

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Q: 5π Determine the exact value of sin- 12

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Q: Analyze the following function with respect to its intercepts, asymptotes, turning points, and…

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A: u=-9i+4jFind -5u.

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (1,1) b. (41)

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Q: (iii) Consider the function C(Q₁, Q₂)=Q-30102+Q2. What level of Q₁ and Q₂ locally minimise this…

A: According to our guidelines , we can answer only first question (due to multiple questions). Kindly…

Q: 9. Given f(x) = x³ - 5x and its derivative f'(x) = 3x² - 5, find the equation of the tangent line to…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: A local business has a Cost function given by of students enrolled. Find the average rate of change…

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Q: 5) Find the Maclaurin series for the function ex

A: Consider the given function .To find the Maclaurin series for the given function.

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Q: 4. Find the local extrema for the given function below. No graphs. f(x) = x + ln(x² + 1)

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Q: M 12 M Let p(x) = x³ – 5x² + 4x − 20. Verify that p(5) the other roots of p(x) = 0 over the complex…

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Q: Find the derivative of the function f(x), FIRST using the Product Rule & SECOND Quotient Rule.…

A: The Product Rule:The Quotient Rule:The Chain Rule:The Power Rule:

Q: 4. x-6 3 a) Determine the point of intersection of the two lines. b) Determine the acute angle…

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Q: State the domain for the function f(x) = In(x + 2) : O (-00, -1) O (-∞, -2) O (-2,00) O (-∞0,00)

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Q: 14. Find the equation of the tangent to the following functions at the indicated point. a)…

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Q: 3a) Determine whether or not the function below is differentiable at O by using the definition of…

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Q: Evaluate the limit. x - 4xy x-4y lim (x,y) → (12,3)

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Q: dy dx = (y +9)(y-9), where y(0) = 8 The partial fraction constants in the partial-fraction method…

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Q: (d²x) Q²: L {1²} dt² =?

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Q: Which of the following graphs is consistent with the differential equation dx = x y

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Q: 3a) Consider the differential equation: y³ (2x+1) sin(x²+x) 2-y³ey (y > 1) Without solving the…

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Q: (a) Consider the first order separable differential equation (2x+3)(y² - 4) dy dx - (i) Find the…

A: Given that, the differential equation is                      (i)

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Q: Multiply. cis (3)cis (2)

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Q: Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared…

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Q: If f(x) = 3x-2 and g(x)=x+1, then (f(g))-¹(a) equals 01-2 O (3-1) O x-1

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Q: Find the maximum value of ƒ(x, y) = x¹y³ for x, y ≥ 0 on the unit circle. fmax =

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Q: Apply the midpoint and trapezoid rule to the following integral. Calculate the approximations and…

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Q: Replace R₂ by (-8)R₁ + R₂. 14-8-7 84 7 8 -5 1 5 2 (-8)R₁ + R₂ = (-8)R₁ + R₂

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Q: Find all the second partial derivatives. sin(3s² - 4t²) V =

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Q: Determine whether the following improper integral converges and, if it does, calculate it: S [Hint:…

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Q: Suppose that h(x) is an unknown function with the following properties: ex x² ● h'(x) - h(1) = 3 Use…

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Q: dQ Use the Chain Rule to find where Q=√√4x²+4y² + 2z², x = sint, y = cost, and z = cost. dt 7 dQ dt…

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Q: Solve the following pure-time differential equation with the given initial condition. X = dx - = sin…

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Q: For the following lines: L₁: x =− 3 + 3t, y =− 1 + 4t and L₂: 2 a) Determine the point of…

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Q: j(x) = x=5 X X 9. j(5) = j(x) 10. lim j(x) as x->5 = 11. j(0) = 12. lim j(x) as x->0 from the left =…

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Q: Your answer is correct. Use sigma notation to write the Taylor series about = ro for the function.…

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Q: 1. Compute the given quantity: ∫∫(2xy)dxdy for x over the interval (0, 2) and y over the interval…

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