please answer all corrrtly.

1)

Use the trapezoidal rule to approximate fox dx, using three non-uniform partitions at {0, 0.25, 1.5, 2}. O (03 + 0.253)(1) + (0.253 + 1.53)(1) + (1.53 + 23)(1) O 0.5[(03 + 0.253)(0.5) + (0.253 + 1.53)(0.5) + (1.53 + 23)(0.5)] O (03 + 0.253)(0.25) + (0.253 + 1.53)(1.25) + (1.53 + 23)(0.5) O o.5[(03 + 0.253)(0.25) + (0.253 + 1.53)(1.25) + (1.53 + 23)(0.5)]Selected values of f' and f", where fis a twice-differentiable function that does not change direction between the given values, are shown in the table. X -6 -4 -2 0 2 4 f'(x) 896 0 -96 -16 10 96 f"(x) -800 -180 32 28 0 140 Which of the following statements is true? Ofhas a local minimum at x = -4 Of has a local maximum at x = -4 Of has a local minimum at x = 2 Of has a local maximum at x = 24x2 + 21 ax = +9 O 4x - 5arctan w / X + C O 4x + 5arctan + C O 4x - 15In x2 +9+C O 4x + 15In x2 +9+CEvaluate sin(3x - 4) dx. O cos(3x - 4) O. -Cos(3x - 4)+ C 3 O L sin(3x - 4) O sin(3x -4)+ CA particle is traveling at a certain velocity modeled by v(t) = 4t, where t is measured in seconds and v is measured in inches per second. How far does the particle travel for 0 s t s 3? O 18 in O 12 in 0 9 in O 3 inDetermine when the velocity equals 0 for an object whose position function is defined as t- = t + 5s' for 0 0 for x -2, then it can be concluded that f has a relative minimum at x = -2. O True, the derivative changes from positive to negative O True, the derivative changes from negative to positive O False, the derivative changes from positive to negative O False, the derivative changes from negative to positiveConsider the function g that is continuous on the interval [- 10, 10] and for which ] g(x)dx = -11. What is ][g(x) + 2]dx equal to? 09 O 20 O-31 O-9Which of the following functions is guaranteed by the Extreme Value Theorem to have an absolute minimum on the interval [-10, 10]? O f ( x ) = x O g(x) = v2x Oh(x) = X- 2 x2 - 4 Oj(x) = cosxA car travels east in a straight path at a speed of 80 miles per hour for 2 hours and then turns around and travels west in a straight path at a speed of 60 miles per hour for 2 hours. Taking direction into account, how many miles is the car from its starting position? O 40 miles 120 miles 160 miles O 280 miles