6. Write the equation of the line that represents the linear approximation to the function f(x) = 12-2² at the point a = 2. Use the linear approximation to estimate f(2.1).

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A: Please see the below picture for detailed solution.

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Q: 9. Determine the domain and range of y = log(2x² - 50) and explain how you know this.

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Q: Question 3 ( Consider the differential equation x²y" - 3xy' + 3y = 2x³ - 3x². (a) Verify that y₁ = x…

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Q: 7. Find a power series representation for the function and determine the interval of convergence.…

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Q: The slope of the tangent line to the curve y = 3 at the point (5,²) I 3 is: The equation of this…

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Q: Obtain the general solution. (HOMOGENOUS EQUATION) 2. xydx(x + 2y)²dy = 0

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Q: Evaluate the definite integral. [² 1 -da 3x² Simplify your answer. Type an integer or a fraction.

A: To find the Integration.

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Q: Use l'Hôpital's Rule to find the following limit. sin (x)-x 3 8x lim x-0

A: SOLUTION-

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Q: Consider the function f(x) = 10x¹0 + 8x5 + 8x5 – 5x³ – 5. Enter the antiderivative of f(x) + C

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Q: Evaluate the definite integral, So x(1-x)182 dx

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Q: - 1 Find ²¹ dz x² +C

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Q: Find a, b, c, and d so that: ab [88] [ c d OA. 98 a b c d -5 3 = Select the correct choice below…

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Q: integral [x³√x² Evaluate the integral √x-2 dx.

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Q: Minimize Q=6x2+2y2​, where x+y=8.

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Q: Solve this differential equation: dy dt y(0) = 2 y(t) = = 0.14y (1 – Y 900

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