The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 48 feet per second is f(t) = −16t2 + 48t + 6.      (a) Verify that f(1) = f(2).                                                                                    (b) According to Rolle’s Theorem, what must the velocity be at some time in the interval (1, 2)? Find that time.

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Q: Find a root of an equation f(x)=x3-x-1 using Newton Raphson method.

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Q: Find the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]

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Q: The height of a ball t seconds after it is thrown upward from a height of 7 feet and with an initial…

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Q: rom the solution provide on #9, how did you get from the 2nd derivative 2 - 2/t3 =0  to 1-1/t3 =0?

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Q: Let f(x) = 18xe - 1s. (a) f'(x) (b) Solve f'(x) = 0 to determine the critical values of f.

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Q: 1.) If the ball IS Thrown. vertically upward with a veloorty of 15 m/s then ts height after t…

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Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: Find a root of an equation f(x) = x^4-2 using Halley's method.

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Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

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Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

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Q: 1. Explain how would you determine the maximum value of y= 1 3-cos x

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Q: A body is projected vertically upward such that is height from the ground in feet is h = 50t –…

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Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

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Q: Once again, a particle travels at velocity t – 1 at time t. Divide the interval 0, 2 into 2k…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.