{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

7.3_1 - SECTION 13 THE NATURAL EXPONENTIAL FUNCTION 267 1...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SECTION 13* THE NATURAL EXPONENTIAL FUNCTION 267 1 83. Iff(:c) = 111(1—0—93), then f'(a:) = 1—1—03’ so f’(0) = 1. Thus, lim 111(1_+\$) = lim M = lim m = f’(0) = 1. \$60 \$ IE—>0 :2: \$90 :1: — 0 7.3* The Natural Exponential Function R 1. (a) e is the number such that 1n 6 = 1. (c) (b) e z 2.71828 The function value at w = 0 is 1 and the slope at a: = 0 is 1. 3. (a) lne‘ﬁzx/i (101131”: (61“2)3=23=8 5-(a)21nx—1 lnm—% —> .1:_e1/2_\/E (b)e_z 5 > m—ln5 —> :c——1n5 1 7.1n(1na:)=1 (i) 61’1“”)261 4:) lnx=e =6 4:; elm=ee <:> {17:68 9.2lnm=ln2+ln(3m—4) => lnm2=1n[2(3m—4)] => Inm2=ln(6w—8) => m2=6m—8 : m2—6m+8=0 => (x—2)(\$—4)=0 => m=2or\$=4,b0tharevalidsolutions. 11. emzCebw 4:1 1ne”=ln[C(ebm)] (i) aw=lnC+bac+lnebm (i) am=lnC+bm (i) 1110 a—b ax—b:c=lnC (i) (a—b)\$=lnC <=> :17: 13. 112+?“ = 100 :> 111 (62W) : 111100 => 2 +511 2 111100 => 5\$ = 111100 — 2 => 0: = gun 100 — 2) 2 0.5210 15.ln(e””—2)—3 —> e"8 2—113 e1_e3+2 => w=ln(es+2)%3.0949 17. (a)e\$<10 : lnem<ln10 => m<ln10 2 m€(—oo;ln10) 1 (b)lna:>—1 => elm>e—1 => m>e_ => w€(1/e,oo) 19. y y ...
View Full Document

{[ snackBarMessage ]}