In Problems 31 and 32, solve the given initial-value problem. 2 4 (_² ) x. -1 (0 31. X'= -(-3) X, X(0) =

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A: given function

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A: We have hx=fgx

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A: We first find f'(x) using exponent rule: [d/dx(x^n)= n*x^(n-1)]

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Q: 24. By suitably renaming the constants and dependent variables in the equations and P' aP(1-aP) I' =…

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Q: 7 Find f(x) if f'(x)= and f(1) = 4. O A. f(x) = -28x-5 +32 -5-3 O B. f(x) = -28x 7 3 O C. f(x) = OD.…

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Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: 6. If f(x)=3x' -+ 4 + 4x +1, find f(x) and f"(x).

A: Given query is to find the Indicated derivative.

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Q: 5. The height of a drone in metres over time in minutes is given by f(x) = 3 - log₂ (x - 1). The…

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Q: 18) Suppose P'(x) = 5ex - 6x³+ 4x and P(0) = -9. Find P(x).

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Q: 33) In Problems 33) through 35), given MB ' (x) = HD(x), HD' (x) = PR (x) , PR' (x) = RB(x) with the…

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Q: 1. If f(x)=−1(7x^2−4)^3 then f′(x)= and f′(−2)=

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Q: 17. Solve the equation x-3x' + 3x +x-6 0

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Q: y = Cax+) ?x5+3 (3メ+)% (4xx+)

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