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Find the partial fraction decomposition. (HINI 3x + 12 x² + 3x For resta decomposition nr:...
* For the function f(x) = (3x + 5 if x 20 6 if x < 0. find f(-10)
5. cot? - 3 = 0 find values 0º < 0 < 360° 6. sin(3x) = 1 find values 0 SX S2
4. Find & such that |--^x=12,< for all \x + 2<8.
Find all values x = a where the function is discontinuous. 3x - 5 if x < 0 f(x) = x2 + 5x -5 if x 20 O A. a = 0 OB. Nowhere O c. a = 5 OD. a = -5
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general solution (for x > 0) of the ODE : Hint: try the change of variables u ≜ x, v ≜ y/x. (c). Find the solution to the ODE that satisfies y(2) = 15. Hint: Try separation of variables. For integration, try partial fraction decomposition. 2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
How : For what values of a, b is gu)-ax+bx, x 23a-b, ocX<2 X72 3X-5 continhows at every X How Apply tépetal Rule liult x-2 X2 x?_u How : For what values of a, b is gu)-ax+bx, x 23a-b, ocX<2 X72 3X-5 continhows at every X How Use the Implicit differentiation to find dy
3x +2 <0 and 4x -320
Find the exact radian solutions in the interval 0 < x < 211 of the equation sinx-cosx-1)(cosx - 3) -0.
Find, with justification, what the absolute maximum value of f(x) = x3 – 3x on the set of real numbers x satisfying x4 + 36 < 13x2. If time does not permit you to finish this question during the exam, please submit what you have and briefly explain what you would have tried.
12. Suppose f(x) is defined as shown below +3 if s 2 f(x) = 3x if x <2 Determine whether or not that f is continuous at 2. 13. Evaluate the following limit.