find maximum and minimum of m(t)= 0.00291^3t + 0.00904t^2 -0.16t +122.81

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Q: 7. Part 2. Evaluate each definite integral using the Fundamental Theorem of Calculus, TT/2 a) (3e* +…

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A: limh→042+h6-256h

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Q: 1. Solve the initial value problem: f(x) = 6 cos x + 2x, F(π) = 2 + π²

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A: Equation of graph is fx=ax3+bx+c

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Q: Find (6x²-7x+4) dx

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Q: 7. Part 2. Evaluate each definite integral using the Fundamental Theorem of Calcul TT/2 a) √ (3e* +…

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Q: Find a potential function for F. 3-4x² 2 y F= 8x y -j {(x,y): y>0}

A: The given conservative vector field is:F=8xyi+3-4x2y2j        (x, y): y>0

Q: 3) Consider the function g(x) = cos(3x). a. Write the first three non-zero terms of the Maclaurin…

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Q: 11. Let on(x)=x" lim 84x for 0≤x≤ 1 and show that So, (0, 0≤x≤ 1, x = 1. 1. n(x) =

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A: Need to find the area bounded by the curves We will use integral to find the area.

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Q: 4) Determine the arc length of the parametric curve r(t) = 3 sin 3t and y(t) = 3 cos 3t for 2 ≤ t ≤…

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Q: 28. ƒ、(2,4) if ƒ(x, y) = xª ln y

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A: De Moivre's Theorem z = r( cosθ + isinθ )then zn = rn( cosnθ + isinnθ ) where r is the modulus θ is…

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A: x = csc( t )y = cot( t )Formula used 1 + cot2x = csc2x

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Q: 5. Use the second-derivative test for local extrema to indicate any local extrema and saddle points…

A: Given   fx,y=x2+y2+6x-8y+10 Concept: The Second Order partial derivative test Let fx,y be a function…

Q: 1. a) Determine the derivative of the function f(x) = 2x² using first principles. b) Use the…

A: Explanation of the answer is as follows