MATH 1300 Lecture 3: MATH 1300 Lecture 3 Notes – Exponential Function and Derivative of the Natural Exponential Function

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1300
• Professor: Shu Xiao Li

Document Summary

Math 1300 lecture 3 notes exponential function and derivative of the natural exponential. (cid:1006) a(cid:374)d (cid:271) (cid:1007): values are stated correct to four decimal places. It appears that the limits exist and: for b=2, for b=3. I(cid:374) (cid:448)ie(cid:449) of the esti(cid:373)ates of f 9s(cid:1004)d fo(cid:396) (cid:271) (cid:1006) a(cid:374)d (cid:271) (cid:1007), it see(cid:373)s (cid:396)easo(cid:374)a(cid:271)le that the(cid:396)e is a number b between 2 and 3 for whi(cid:272)h f 9s(cid:1004)d (cid:1005). It is traditional to denote this value by the letter e. If (cid:449)e put (cid:271) e a(cid:374)d, the(cid:396)efo(cid:396)e, f 9s(cid:1004)d (cid:1005) i(cid:374) e(cid:395)uatio(cid:374) (cid:1008), it (cid:271)e(cid:272)o(cid:373)es the follo(cid:449)i(cid:374)g important differentiation formula. Derivative of the natural exponential function: thus the e(cid:454)po(cid:374)e(cid:374)tial fu(cid:374)(cid:272)tio(cid:374) f s(cid:454)d e(cid:454) has the p(cid:396)ope(cid:396)t(cid:455) that it is its o(cid:449)(cid:374) de(cid:396)i(cid:448)ati(cid:448)e. The geometrical significance of this fact is that the slope of a tangent line to the curve y. Ex is equal to the y-coordinate of the point: example.