We have the differencial equation: a' = sin(t + x), x(0) = 1/2. a" (t) Find by taking the derivative on both sides and then find a" (0) t = 0.1 Use this to find a solution approximation at by using the quadratic taylor polynomial. Also find a h that guarantees an error less than 0.0001 when using Eulers method.

Q: Find the 1st derivative of the following. Differentiate implicitly. Simplify your final answer but…

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Q: Find y as a function of x if y(1) = 8, y′(1) = 6. y = x²y" — 6xy' – 8y = 0,

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Q: nd the hundredth derivative of p (x) = (x + x + x')1°(1 + x²)'' (x³ + x° + x'). Justify your answer.

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Q: 4. Find y'(x) for x²y² – 2x = 4 – 4y. Then find the equation of the tangent line at (2, –2 _n…

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Q: Use Newton's method to approximate a root of the equation 4x' + 5x* + 4 = 0 as follows. Let x1 = 3…

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Q: 14x10 14x10 - 2100f 1. The velocity of a rocket is given by v(t) = 2000 ln -9.8t,0<t<30 where v is…

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Q: Find the second derivative of the following function at x = 2 y = (x +) 2 G+x)

A: Given function is y=x+1x2

Q: 3. Let f(x) = (3x² + 1)2. Find f'(x) in 3 different ways by following the instructions below in…

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Q: y' = 3√y + 6x³ 3

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Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

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Q: For the function f(x) = 7x° – 5x + 2x + 7, find f''(x). Then find f''(0) and f"(5). f'"(x) = Select…

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Q: Given that y= 6t^3 +1 and x = t^2-1. Find y’ when x=6

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Q: 2 Given f(x)=esinx In√x (a) (b) Find f'(0.8) by using 2-Point Forward Difference, 2-Point Backward…

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Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

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Q: Let f(x) = 4x - 32√x and a = 4. Compute f'(x) and find an equation for the tangent line to the graph…

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Q: Find the equation of the tangent line at (1, f(1)) when f(1) = 4 and f'(1) = 3. (Use symbolic…

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Q: 1) Find the derivative of f(x)= 2x³+ 2x +12. Then evaluate the

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

Q: given f(x)= 7x+11/5x+2 a.) find df/dx: -41/(5x+2)^2 b.) find the equation of the tangent line when…

A: The given function is: fx=7x+115x+2You have already found f'x which is -415x+22.Now, we need to find…