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# Study guide for exam 1 Math 1610-090

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This 5 page Study Guide was uploaded by Nikki Bee on Wednesday June 10, 2015. The Study Guide belongs to Math 1610-090 at Purdue University taught by in Spring 2015. Since its upload, it has received 98 views. For similar materials see Calculus 1 in Math at Purdue University.

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Date Created: 06/10/15

H EL Spring 2015 MA 16100 Study Guide Exam 1 Review of AlgebraPreCalculus a Distance between P11 yl and Pa2 yg is PQ 12 x12 I y2 y12 b Equations of lines i Point Slope Form y y1 2 7725 511 ii Slope Intercept Form y 2 ma b 1 C L1L2 42gt m1 m2 L1 1L2 4 m2 1 d Equation of a circle a h2 y k2 r2 e Determining domain of a function f Transformations of Functions y f 39lt yfxc I Vertical Shift 0 gt 0 yfx a y c gt shift vertically 0 units up b y 0 gt shift vertically 0 units down yfxc r r KKK II Horizontal Shift 0 gt 0 a y f a 0 gt shift f horizontally 0 units right b y f a c gt shift f horizontally 0 units left Y yf X39I39C Yf x Yf x c V v X C III Vertical Stretch Shrink c gt 0 y 2 cf gt stretch f vertically by a factor 0 If c lt 17 this shrinks the graph Y ycfx Yf X yfun IV Horizontal Stretch Shrink c gt 0 37 Q y f E gt stretch f horizontally by a factor 0 If c lt 17 this shrinks graph 0 Y taquotquoti7 0 l l V Re ections y f m x yfcx Yf x a y f1 gt reflect about az aXis b y f 1 gt reflect about y aXis Y yf x yfx x 0 NH Combinations of functions composite function f o f y 6 exponential functions y a a gt 0 xed agt1 0ltalt1 Y Y x 3 x a Y1 o x LaW of Exponents One to one functions Horizontal Line Test inverse functions nding the inverse f11 of a 1 1 function f graphing inverse functions yf391x yx yfx x E Logarithmic functions to base a y loga 1 a gt 07 a 7E 1 agt1 0ltalt1 y Y y1oga x y1oga x 01 x 0N Logarithm formulas logaxzy ltgt ayza logaam 3 for everya E R alogam 3 for everya gt 0 Law of Logarithms Finite Limits a lim L gta b m gta C lim f L left hand limit gta logawy loga a loga y loga loga 3917 loga y y 10ga93p p loga a lim f L right hand limit Yf x Yf x Yf x Recall gta limf1L ltgt lim lim faL m gta gta 10 In nite Limits a lim 00 gta b lim 00 m gta 0 lim 00 gta Remark The line 1 a is a Vertical Asymptote of f if at least one of lim f m gta or lim is 00 or 00 gta Yf X w l N yf x RF or lim f m m l 11 12 13 Limit Laws computing limits using Limit Laws 2 lim h2a L ar ia SQUEEZE THEOREM If h1a S S h2a and lim h1a a gta then lim L a gta f a f continuous on an interval f continuous from the t f continuous at a ie lim ar ia left at a ie lim ar ia jump discontinuity removable discontinuity in nite discontinuity Y f a or continuous from the right at a ie lim f a gta Yf x quotgt x removable discontinuity infinite discontinuity Jump discontinuity LIMIT COMPOSITION THEOREM If f is continuous at b Where lim 95 2 b then 91133 fgw f 91133 gm my Limits at In nity ggfL wgtggg L Y F m m L x w L x 14 15 Remark The line y L is a Horizontal Asymptote of f E Z 332 f331 Average rate of change of y f over the interval 511 512 39 39 A3 332 511 slope of secant line through two points average velocity De nition of derivative of y f h at a f a lim flta a or equivalently f a lim M interpretation h gt0 h ac m a a of derivative slope of tangent line the graph of y f at a velocity at time a fWU instantaneous rate of change of f at a d y differentiable functions ie d3 Derivative as a function f lim gt0 1quot exists higher order derivatives f mf h d2y d332n

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