Equations and functions

Extract

[...] Equations and functions 1a) - must be continuous on the closed interval 2]. - must be differentiable on the open interval Using the MVT equation: 1b) Equating to c = For x = ? is increasing on the interval For x = ? is decreasing on the interval 3). For x = ? is increasing on the interval V = s^3 = 0.93s^3 = s (0.93) ^ %decrease = - * 100 %decrease ~ 2.44% Quotient Rule on the left side: = ² Quotient Rule on the right side: = 0 ² = (2xy - x²) dy/dx * y² Multiply by ² y² dy/dx= (2x^3y - 4x²y² + 4y^3) ²) Product rule: = u'v + uv' = 4(3x + * 3 = 12(3x + = 3(6x - ² * 6 = 18(6x - ² x = x = 1/6 7a) x = sin?/?3 da = cos?/?3 Pythagorean identity: cos²(?) = 1 - sin²(?) 7b) For ? [...]

[...] log_a(x-1) + log_a(?x-1) log_a(?x-1) can be written as: ½ . log_a(x-1) = 3/2. log_a(x-1) 12b) Log_3(27) = 3 log_8(2) = log_5(25) = 2 We add the terms: = 3/3 + 1/3 = 4/3 13a) Where: = x² Product rule: 13b) u = ln + bx + cx²) Then, y = u² dy/dx = 2ln + bx + cx²) * + 2cx) / + bx + cx²) dp/dt = kP Where k is a proportionality constant. = P_0 P = 3P_0 ? [...]

[...] Since the acceleration is a constant and the point is always accelerating to the left. Thus, there is no time interval where the point is accelerating to the right. A point slows down when its velocity and acceleration have opposite signs. Thus, the point is slowing down when: > 0 and [...]