AP Calculus Flash Cards Exam Questions with Correct Grade A+ Solutions

AP Calculus Flash Cards Exam Questions with Correct Grade A+ Solutions 1 - Correct Answers: 0 - Correct Answers: Squeeze Theorem - Correct Answers: f is continuous at x=c if... - Correct Answers: Intermediate Value Theorem - Correct Answers: If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k Global Definition of a Derivative - Correct Answers: Alternative Definition of a Derivative - Correct Answers: f '(x) is the limit of the following difference quotient as x approaches c nx^(n-1) - Correct Answers: 1 - Correct Answers: cf'(x) - Correct Answers: f'(x)+g'(x) - Correct Answers: The position function OR s(t) - Correct Answers: f'(x)-g'(x) - Correct Answers: uvw'+uv'w+u'vw - Correct Answers: cos(x) - Correct Answers: -sin(x) - Correct Answers: sec²(x) - Correct Answers: -csc²(x) - Correct Answers: sec(x)tan(x) - Correct Answers: dy/dx - Correct Answers: f'(g(x))g'(x) - Correct Answers: Extreme Value Theorem - Correct Answers: If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval. Critical Number - Correct Answers: If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined) Rolle's Theorem - Correct Answers: Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval). Mean Value Theorem - Correct Answers: The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line. First Derivative Test for local extrema - Correct Answers: Point of inflection at x=k - Correct Answers: Combo Test for local extrema - Correct Answers: If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c. If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c. Horizontal Asymptote - Correct Answers: L'Hopital's Rule - Correct Answers: x+c - Correct Answers: sin(x)+C - Correct Answers: -cos(x)+C - Correct Answers: tan(x)+C - Correct Answers: -cot(x)+C - Correct Answers: sec(x)+C - Correct Answers: -csc(x)+C - Correct Answers: Fundamental Theorem of Calculus #1 - Correct Answers: The definite integral of a rate of change is the total change in the original function. Fundamental Theorem of Calculus #2 - Correct Answers: Mean Value Theorem for integrals or the average value of a functions - Correct Answers: ln(x)+C - Correct Answers: -ln(cosx)+C = ln(secx)+C - Correct Answers: hint: tanu = sinu/cosu ln(sinx)+C = -ln(cscx)+C - Correct Answers: ln(secx+tanx)+C = -ln(secx-tanx)+C - Correct Answers: ln(cscx+cotx)+C = -ln(cscx-cotx)+C - Correct Answers: If f and g are inverses of each other, g'(x) - Correct Answers: Exponential growth (use N= ) - Correct Answers: Area under a curve - Correct Answers: Formula for Disk Method - Correct Answers: Axis of rotation is a boundary of the region. Formula for Washer Method - Correct Answers: Axis of rotation is not a boundary of the region. Inverse Secant Antiderivative - Correct Answers: Inverse Tangent Antiderivative - Correct Answers: Inverse Sine Antiderivative - Correct Answers: Derivative of eⁿ - Correct Answers: ln(a)*aⁿ+C - Correct Answers: Derivative of ln(u) - Correct Answers: Antiderivative of f(x) from [a,b] - Correct Answers: Opposite Antiderivatives - Correct Answers: Antiderivative of xⁿ - Correct Answers: Adding or subtracting antiderivatives - Correct Answers: Constants in integrals - Correct Answers: Identity function - Correct Answers: D: (-∞,+∞) R: (-∞,+∞) Squaring function - Correct Answers: D: (-∞,+∞) R: (o,+∞) Cubing function - Correct Answers: D: (-∞,+∞) R: (-∞,+∞) Reciprocal function - Correct Answers: D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero Square root function - Correct Answers: D: (0,+∞) R: (0,+∞) Exponential function - Correct Answers: D: (-∞,+∞) R: (0,+∞) Natural log function - Correct Answers: D: (0,+∞) R: (-∞,+∞) Sine function - Correct Answers: D: (-∞,+∞) R: [-1,1] Cosine function - Correct Answers: D: (-∞,+∞) R: [-1,1] Absolute value function - Correct Answers: D: (-∞,+∞) R: [0,+∞) Greatest integer function - Correct Answers: D: (-∞,+∞) R: (-∞,+∞) Logistic function - Correct Answers: D: (-∞,+∞) R: (0, 1) Given f(x): Is f continuous @ C Is f' continuous @ C - Correct Answers: Yes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp Given f'(x): Is f continuous @ c? Is there an inflection point on f @ C? - Correct Answers: This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes. Yes f' decreases on X<C so f''<0 f' increases on X>C so f''>0 A point of inflection happens on a sign change at f''