dx & lim

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } m tangent = find equation of secant line acceleration speed velocity speed- absolute value of velocity; does not have direction; magnitude component of velocity- rate of change of position- distance moved per unit of time - s(t) = position fxn velocity- contains both magnitude + direction- s'(t) = velocity fxn acceleration- rate of change of velocity- s"(t) = acceleration nfxn define derivative of a function how is continuity of a function related to limit? f(x) is continuous at x = a when: squeeze theorem: range of sin: [-1,1] lim as x goes to 0: 0 < 0 < 0 squeeze theorem: derive formulas for: circle - circumference - area sector - length - area  sphere - volume - area circle sector sphere intermed value therem function continuous over closed interval [a, b]if :for any value d between f(a) & f(b), excluding f(a) & f(b), there is a c between (a,b) such that f(c) = d  = 0 r is a positive rational numberif r > 0 & x > 0, x^r will go to infinity, & 1/x^r will approach 0 principal values of inverse trig fxns prove:    substitute   factor out c = c f'(x) prove difference between essential, non-essential, & removal discontinuity essential: can't be patched; graph has a break:(2,3) & (2, 5) breaks at x = 2 non-essential: removable discontinuity, can be patched,  if these are = (both 9), can patch by defining f(3) = 9 what must be true to repair a discontinuity? the 2 one-sided limits must be the same: the limit of f(x) as x approaches c from the left and right must be equal then f(x) can be repaired by defining f(c) = L methods for finding/evaluating limit of a fxn using table of values as x gets closer & closer to agraphicallyalgebraically using limit lawsusing trig identities if f(x) 2: is in domain of f(x)f & g are continuous interval continuity f(x) is continuous on an interval if it is continuous at q # in the intervalif f is defined on only one side of an endpoint, continuous at the endpoint means continuous from the right or continuous from the left the line y = L is a horizontal asymptote of the curve y = f(x) if: either: .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorjojobean0203 ID203202 Card Setdx & lim Descriptiondx Updated2013-05-27T23:28:57Z Show Answers