calc notes, test 1

calc notes, test 1 - Lim sin x = sin c (for sin, cos, tan,...

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Testing for Symmetry Y-axis: (x,y) and (-x,y) are points on the graph X-axis: (x,y) and (x,-y) are points on the graph Origin: (x,y) and (-x,-y) are points on the graph Even/Odd Functions Even: When symmetric to y-axis Odd: When symmetric to origin If a graph is symmetric to the x-axis then it isn't a function, Y = 0 : only function Functions must pass 'vertical line test' Reflection (x-axis): y = -f(x) Reflection (y-axis): y = f(-x) Reflection (origin): y = -f(-x) Inverse function: switch x and y then solve for y Function only has an inverse if it passes the 'horizontal line test' Y = arcsin x means sin y =x and -p/2≤y≤p/2 Inverse of secant: Arcsec a = y; means, secant y = a and (restriction on y) Cos y = 1/sec y = 1/a; cos y = 1/a; or y = arccos 1/a Inverse of secant: Arcsec a = y; means, secant y = a and (restriction on y) Cos y = 1/sec y = 1/a; cos y = 1/a; or y = arccos 1/a Limits of transcendental functions
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Unformatted text preview: Lim sin x = sin c (for sin, cos, tan, csc, sec, cot & ln) Lim sin x/ x =1 x-> 0 Lim (1- cos x)/x = 0 x->0 Lim (1+x)1/x = e x->0 Continuity: being able to draw a function w/o picking up pencil Ex of not continuity: open circle, stop start somewhere else, etc ; Closed interval = brackets, open interval = parenthesis Not continuous: open dot, lines not connected, open dot on line, solid dot not on line Removable discontinuity: can be found using a limit; Nonremoveable discontinuity: limit doesnt agree (ex. Two lines approaching different points) One Sided limits: lim (x c) f(x) = L right means that x approaches c from values greater than c: x c + left values less than c: x c- limit DNE: limit from left doesnt equal limit from right Greatest Interger: [[x]] = greatest integer n such that n x; [[2.5]] = 2 and [[-2.5]] = -3...
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