Calculus Final Exam Questions with Correct Answers

Vertical Asymptote - ANSWER-Set Denominator equal to zero Horizontal asymptote - ANSWER-set numerator equal to zero Rolles theorem states there is... - ANSWER-a tangent line at some point on a closed interval [a,b] if the following hold true a) continuous b) differentiable c) f(a)=f(b) Integration is a... - ANSWER-continuous addition process Intermediate Value Theorem: Suppose f is a function continuous at every point on the interval [a,b]: - ANSWER-a) f will take on every value between f(a) and f(b) over the interval b) For any L between the values f(a) and f(b) there exists a c in [a,b] for which f(c)=L Mean value theorem: if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then... - ANSWER-a) there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b] Mvt: slope of tangent line f'(c) = - ANSWER-slope of secant line: f(b) - f(a) / b-a Critical points... - ANSWER-occur when derivative doesn't exist or equals 0 Local extrema is... - ANSWER-the point at which a max or min value of the function in some open interval containing the point is obtained If f(x) is continuous function on [a,b] then, the integral from b to a of f(x): - ANSWER-area above x-axis and below curve - area below x-axis and above curve To find average of definite integral multiply by: - ANSWER-1/b-a FTC pt. 2 holds if... - ANSWER-f(x) is continuous over the interval [a,b] F(x) is an antiderivative of f(x) If f(x) is continuous over an interval [a,b] then there is at least one point c in [a,b] such that... - ANSWER-f(c) = 1/b-a integral from b to a of f(x)dx