# File0031 - EXEIEiSES SECIION 7.3 THE NATURAL EXPOIIENTlAl...

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Unformatted text preview: , EXEIEiSES SECIION 7 .3* THE NATURAL EXPOIIENTlAl FU’NCIIOII ’ 465 w 15 the number 2 deﬁned? at is an approximate Value for e ? . tab, by hand, the graph of the function f (x) = exwith 'cular attention to how the graph crosses the y-axis. ‘ (at fact allows you to do this? 'lify each expression. , (b) In J2 (b) e 3 1n 2 (b) eﬁ =5 (1)) ln(5_ - 2x) = —3 b" where a 3i b I=12 'd the solution of the equation correct to four decimal l4. 1n(l M/i) : 2 l6. NH) : 7 lve each inequality for x. '10 (b) lnx> —1 lnx < 9 (b) 22—“ > 4 r.’ u n n n “ ake a rough sketch of the graph of each function. Do ‘ eulatnr. Just use the graph'given in Figure 2’ and, if e transformations of Section 1.3. 20.y=1‘ 22. y=27 a n n with the graph of y = 6", write the equation of the results from _' g2 units downward g 2 units to the right (c) reﬂecting about the x-axis (d) reﬂecting about the y-axis‘ » (e) reﬂecting about the x—axis and then" about the y-axis . Starting with the graph of y = e", ﬁnd the equation of the graph that results from ‘ L (a) reﬂecting about the line y = 4 ' (b) reﬂecting about the line x = 2 25—30 Ill] Find the limit. 25. lim 8"” 26. lim em" xam _ xﬁ (11/2)1L 27 . 83x _ e’SX 23 1- 63): __ 6A3; . 11m ————3x ,3): - -im 3, +‘ —3x- me e + e _ we” e 29. lim 8/0"” 30. unisex/(2“) 1,—>Z‘ X—VZ" n u < n ~ n l: 31-44 Ill] Differentiate the function. x e 3]; f(x) = xze" L ‘V y = 1+ x .33- y = 6"”3 y = e“(cos u + cu) 35. ﬂu) = M 31.1:(t) = am y = emu 39. y = 1/1 +33% yze‘lnx y = cos(e’”) Fin—+73 e‘ + 6" 45-46 ml Find an equation of the tangent line to the curve at the given point. 45. y = 62‘ cos 77x, ’(0, l) ‘46-. y #— ex/x, (1, e) 47. Find y’ if 6ny = x +31. 48. Show that the function y ¥ Ae"" + Bxe” satisﬁes the differen- tial equation y” + Zy’ + y = 0. 49. [For what values of r does the function y = e” satisfy the equav tion y” + 6y’ + 8y = 0? ' 50. Find the values of A for which y = 9’” satisﬁes the equation y + y' = y”. 51; If f (x) = e“, ﬁnd a formula for f ("’(x). 52. Find the thousandth derivative of f (x) = xc". ...
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