Find f. f"(x) = 6 + 6x + 36x², f(0) = 3, f(1) = 14

Q: the of Sketch the graph of the ellipse defined by each following equations Transform the equation to…

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Q: Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product…

A: c'(x)=-30x2+110formula for average cost is  c=∫c'(x)dx∫xndx=xn+1n+1+c

Q: Answer the following questions for the function f(x)=x√x² +36 defined on the interval -5 ≤ x ≤ 6.…

A: The function is given as , fx=xx2+36 on -5≤x≤6

Q: Consider the function f(x) = 12x5 + 30x¹ - 160x³ +3. f(x) has inflection points at (reading from…

A: We need to find out the inflection points.

Q: Part 2. Solve 2 cos² (0) + sin(0) = 1.

A: tanx=3, -2π≤ x≤2π

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Q: Find the particular solution to the differential equation. dy = y² when x = 1, y = 2 2xy +4

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Q: Find the volume of the solid that lies under the paraboloid z = 6²-2² - y² and above region R={(r,…

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Q: K Consider the function f(x)= 3 x + 3x (a) Evaluate lim f(x) and lim f(x), then identify the…

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Q: Find the equation of the ellipse that satisfies the given conditions. Foci: (-1, 1) and (-1, 3);…

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Q: y = 12²2 × √√ x²-16 - 8 In (x + √√x²-16)

A: Given :y=12xx2-16-8lnx+x2-16

Q: Brisk Basic rules (sum, product, quotient, power) DO NOT USE THE DEFINITION olin. anymore. Use the…

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Q: Find the interval of convergence for the power series. a b. c. 00 Σπ=o 100 τ (-1)*(x+1)π 2" Sn Σ…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: 3. Given sin(A) = in Quadrant 1 and cos(B) = -in Quadrant 3, find sin(A + B). Leave your answer in…

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Q: If θ=5π/4, then find exact values for the following: sec(θ) equals=    csc(θ) equals=…

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Q: Find f(x) such that f'(x) = e7x - 6x and f(0) = 10.

A: f'(x)=e7x-6xf(0)=10f(x)=∫(e7x-6x)dx∫xndx=xn+1n+1+c

Q: Find the exact value of each of the remaining trigonometric functions of 0. 21 sin 0 = 0 in Quadrant…

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Q: The rate at which a battery charges is slower the closer the battery is to its maximum charge Co.…

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Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

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Q: Use a reference angle to find the exact value of the following expression. Do not use a calculator.…

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Q: ind the local maxima and minima for the function f(x) = |x² + 3x − 4. If there is more than one…

A: solution is given below.

Q: Given: (x is number of items) Demand function: d(x) = = 2880 x Supply function: s(x) = 5√x Find the…

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Q: Find y Y = ex 2 X

A: Given query is to find the derivative.

Q: Find the equation of a hyperbola that satisfies the given conditions. Vertices (0, 2), (0, -2);…

A: GivenThe vertices of hyperbola is (0,±2) and asymptote is y=±23x   We need to find the equation of…

Q: Which of the following is (are) equivalent to e¹2t? Select all that apply. O e¹2 et □ (e¹2)t O…

A: Given that e12t To determine which are equivalent to e12t

Q: L {5-e²t +6t2} L {t²-3t 2e sin(3t)} MA L {t-t²-t+sin(√2t)} D

A: The answer is given below: Topic: Laplace transformation

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: Suppose that f(x, y) = e²/y on the domain D = D Q Then the double integral of f(x, y) over D is ₁…

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Q: Use the Ratio Test to determine whether ∞     n = 1an converges, where an is given. State if the…

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Q: Prove whether the following integral converges or diverges: 1 S₁Ⓡ dx In(x) x

A: ∫xndx=xn+1n+1+cd dx(lnx=1x

Q: You measure the angle from the ground to the top of the building from a point 79 feet away from the…

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Q: lim x²+3x-5 2x³²-=-5x+7

A: The limit value of given function is  L=1/2

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² = 36 and…

A: we need to find the volume of the wedge-shaped region.

Q: Estimate the areas under the curve by computing the left Riemann sum L₂.

A: From the given graph, we have to find the area under the graph using the Left Riemann sum.

Q: Given cos(x)= O √ NIET NI → 2 - IN 2 what is the value of cos(x + TT)?

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Q: Suppose f (a) g म (b) h 3 T 3 n' (3) = 2 and f' π 3 = -7. Let g(x) = = f(x) sin(x) and h(x) = cos(x)…

A: To find out the derivatives.

Q: For each part, type your answer in as a fraction. Do not use a decimal or round your answers. If…

A: We need to find out csc(x), sec(x), cot(x) for the given trigonometric functions.

Q: Evaluate the integral. (Remember the constant of integration. Remember to use absolute values where…

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Q: Let f(x) = be a differentiable function with f'(x) > 5 on the interval [−1,8]. If ƒ(8) = -5, what is…

A: we need to find the largest possible value of f(-1).

Q: 2) Draw an expansion path in which it becomes cheaper for a firm to use K as it gets bigger.

A: We know that the production function of the firm: q=f(x,y) which gives us the isoquant map of the…

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Q: Solve (5x - 3y + 4z = 12 x+y=2z = 8

A: We will use elementary row operations on augmented matrix to find the solution.

Q: $5000 is invested in an account that pays interest of 4% compounded daily. What will the account be…

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Q: 3. 1+x 1+x² dx

A: Topic = Integration

Q: Find the general solution to the given differential equation. (Remember the constant of integration…

A: dx=x7ydy∫xndx=xn+1n+1+c

Q: 3. f xsin(x²)dx √1+cos(x²)

A: Topic = Integration

Q: lim (2x-1)(3-x) (x-1)(x+3) is

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Q: 2 cos²x + 7 smx-5=0 on on [012]

A: