Write f(x)=3x^3-3x in terms of y

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. sin(In 41x) X dx

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Q: 6. Condense the logarithmic expression into a single logarithm. log(t)-2 log(w-1) + log(t + 1)

A: We can condense the logarithmic expression in the below steps.

Q: 1. Simplify the following expressions without the aid of a calculator. a) log, (81) b) log2 (2525) -…

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Q: Evaluate i. Integral 6xln(3x^2+5)dx by selecting and using appropriate substitution.

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Q: CALCULUS

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Q: Problem 2. Consider the region R bounded by the the graphs of y = 4 - x², and y = x² - 2x. Sketch…

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Q: Evaluate f'(x) if f(x) = x¹nx¸ 2 lnx lnx [A] ·X² x In [B] x xnx 2 [C] 2 ln x x ·x² [D] 0 [E] 2 ln…

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Q: 6) F(x) - (23x44) (x2 Sinx + 3x) + 3x)

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Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

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Q: Question 1 Find the transform of the given function by use of a table. f(t) = cos -4t-sin-4t (A)…

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Q: Calculate the consumer's surplus at unit price ō = 10 for the demand equation q=20 -0.05p²

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Q: A particle moves along the curve implicitly defined by xy¹ - yx4 = x-y2. When the particle passes…

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Q: 1. We are interested in evaluating the integral 3 [√9-2² dr. Note that this integral gives you the…

A: Given: ∫039-x2dx a ) Let fx = 9-x2 Using Riemann sum with 3 rectangles and right-hand endpoints we…

Q: An object thrown vertically upward from the surface of a celestial body at a velocity of 12 meters…

A: Solution ) s(t) = -6t2 + 12t  Differentiate  with respect to t  s'(t) = - 6 × 2t + 12  [ formula…

Q: 9. A Rectangular box w/an open top is to be made from a square piece of cardboard that is Binche's…

A: This question can be solved using the concept of maxima and minima.

Q: Let y = f(x) = = e -10x ¹+1 Find the equation y = T(x) of the tangent line of the inverse of fat (1,…

A: Given that , y=fx=e-10xx4+1 find the equation of the tangent line of inverse of f at 1,0.

Q: π/4 de Evaluate the integral √ (secx + cos x)² dx LENT O blen

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Q: Find the Inverse Laplace Transform of (2s-5)/(s2 + 2s + 10) O 2e^-tcos3t+ (7/3)e^-tsin3t)…

A: As we know the inverse Laplace transform identity. 1). L-1s-as-a2+b2=eatcosbt 2).…

Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: cos8x-1 sin8x 4.Evaluate y' for y=- and simplify the answer

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Q: Let z(x, y) = x³y where x = Calculate da dt = t³ & y = 1⁹. = dz dx dy by first finding & and using…

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Q: Find the solution of the nonhomogeneous linear differential equation using the method of…

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Q: Find the indefinite integral. (6x + 1)-9dx

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Q: A current state has a population of 3500. With the rate of 0.23/year, what will be the population…

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Q: dy Find for the equation ex+y² = x. dx 3-x [A] [B] ³ xy 1-x 2xy [C] 1-2x xy [D] 2-x 2xy+e [E] 1-x xy

A: Concept: The formulas used: ddxxn=nxn-1ddxln(x)=1xln(ab)=bln(a)

Q: Use the properties of logarithms to exapnd the logarithm as much as possible: 4 log5 ພາ2 x4y³

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = [0, 9] X x²…

A: topic - Application of derivatives We are given, f(x)=xx2+25  ,[0,9]we know…

Q: If y satisfies dy dx 2xex², = then (a) y(In e) = (b) y(In e²) = y (0) = 1,

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Q: Implicit Differentiation using f, fy & f Let 20x² 1 dy dr dy Use partial derivatives to calculate at…

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Q: 2. The area of Mammoth Cave Nationc Park in Kentucky is about seventy-four thousand, nine hundred…

A: We have given the area of the which is "Seventy-four thousand, nine hundred thirty and sixteen…

Q: torgent 2. A particle moves along the curve implicitly defined by x²y³ + yx³ = x² - y². When the…

A: Differentiate wrt t  and put value

Q: i. S 6x ln(3x² + 5) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Solve the given Exact Equation. Be sure to supply all the steps that lead to your answer. (cos x cos…

A: To solve the differential equation.

Q: Determine whether f(x) = = -4x² + 16x - 2 has a minimum or maximum value, and find the value of the…

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Q: 1+t² e. y' = tye-t

A: We need to determine D.E. is separable or not.

Q: 5 T²S²³² Evaluate Answer: zx^hx xy√x² + y² dy dx.

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Q: 2. In(2x² + y); x = √i, y = 12/3

A: Need to find out the derivative.

Q: x + 3y s 18 2x + yΣ 14 x Σ Ο Υ Σ Ο

A: See this solution in below.

Q: Y Calculate J₂ (₁2) dA JR 1 + x R= [0, 5] x [0, 5]. Answer: dA, where

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Q: The general solution to the DE in the initial value problem (IVP) 4 (y" + 6y' +9y = 0 y (0) = 1…

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Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid in the…

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Q: Put the equation y = x² - 4x + 3 into the form y = (x - h)² + k: Answer: y = Question Help: Video…

A: Given query is to find the vertex form of parabola.

Q: Find the intercepts of f(x) = −2(x + 2)(x − 5)(x+4) . Enter intercepts as points. If you have more…

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Q: Determine all equilibrium solutions and classify as stable, semi- stable, or unstable. dx dt a. b.…

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Q: 20. Evaluate the limit or show that the limit does not exist. Show proper work. sin y cos y ye (a)…

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Q: 2x^2-4x+1/4x^2+1 determine the limit of n----> infinity an

A: Given query is to find the limit of the expression.

Q: 3. Rewrite the logarithmic equation log416 = as an exponential equation. 4. Rewrite the exponential…

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Q: 1. When you swim underwater, the pressure in your ears depends on the depth at which you are…

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Q: Describe the method used to integrate sin ³x. Choose the correct answer below. O A. Rewrite sin ³x…

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