Mastering Exponential & Logarithmic Limits, Study notes of Mathematics

Download Mastering Exponential & Logarithmic Limits and more Study notes Mathematics in PDF only on Docsity!

To find the limit. oF A Funchon Using its araph, we follow these steps : 1. Ooseve tne behavior o¢ the graph AS X approaches From the let and right cides. ; a 2, Echmate the value that the fonction approaches as x approaches Se es \o = g “J -¢-4-2 0) 2 4 6 TR graph shows that as x becomes Closer to KX =2Z. prom the leet andl right sides, the yalve of the Function appeoaches 4. Hence, boiced on thé onentiar| The Amit of an 2X7: _ is the exponential function o¢-the mit _ op Ae Function. © cas) SS “2 The limit cpan ¢xponental Function F(X) = b2®) where glx) is-a polyno. # mial in x, as X approaches ¢ is eqqual i eo , lim ae): pre) X26 a is ay Note. thet an exponential Fonction is deginect porany ‘rea numberc, Thus, lie B9OV_ L302) SENG Prooe 4 : ees Let ¢(e< pO) where qo iat polynomial inx, be an exponential “ ponetion, and ¢ is a real number, An eAponential unction 18 dé¢ined Fer. any real number C. Using the propery of limit ForeéxponenHal. .B ee a lim ¢O)= limbIO lima) XC XG sa fate. . fi *dna@)= ole) stole is lim eG2= pe 0s): ® =e x inches ~ Thecegore, i¢ ¢02) 18 an exponcotinl ge hehe ey 6) - tx: lim 3 2 32 ; pi ie: = Shenae Sin & is he ie, Sle Gh a ER ea & > Thi¢ theorem holds re as. Nell for MS Pi Eausaina Funchon oe. base. ‘ & (Euler. number); which is a nonterminating and nontepeating = deamals We call it he natvral Mae “The. graph shows ist as x Joecomes - closer to X=4 From the {ecb and ri icles, the value oF We mcion app poachts. oe, Henet, based on the vn 5 . We estimate sa Mire my taa: E PRo pERTY OF WMT FOR Loga= d -RiTaMne pene