# Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals

Pupil ideas guide for Stewart's unmarried Variable Calculus: Early Transcendentals [Paperback] [Jan 01, 2008] Daniel Anderson, Jeffery Cole, Daniel Drucker

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This restrict has the shape 00 . lim x→0 sech2 zero 1 tanh x H sech 2 x = = =1 = lim x→0 tan x x→0 sec2 x sec2 zero 1 23. This restrict has the shape 00 . lim 25. This restrict has the shape 00 . lim 5t − 3t H 5t ln five − 3t ln three = ln five − ln three = ln fifty three = lim t→0 t 1 27. This restrict has the shape 00 . lim √ 1 sin−1 x H 1/ 1 − x2 1 = lim √ = lim = =1 x→0 x→0 x 1 1 1 − x2 29. This restrict has the shape 00 . lim 1 − cos x H sin x H cos x 1 = = lim = lim x→0 2x x→0 x2 2 2 t→0 x→0 x→0 31. lim x→0 0+0 zero x + sin x = = = zero. L’Hospital’s Rule doesn't practice.

34 swap in strain = = zero. 434. utilizing P for strain and d for intensity with the purpose 10 toes switch extensive 10 (d, P ) = (0, 15), we have now the slope-intercept type of the road, P = zero. 434d + 15. (b) whilst P = a hundred, then a hundred = zero. 434d + 15 ⇔ zero. 434d = eighty five ⇔ d = eighty five zero. 434 ≈ 195. eighty five ft. therefore, the strain is a hundred lb/in2 at a intensity of roughly 196 toes. 19. (a) the information seem to be periodic and a sine or cosine functionality may make the simplest version. A version of the shape f (x) = a cos(bx) + c turns out applicable.

F. neighborhood greatest worth f (−1) = 2, neighborhood minimal price f (1) = −2 G. f 00 (x) = 23 x−5/3 < zero while x < zero and f 00 (x) > zero while x > zero, so f is CD on (−∞, zero) and CU on (0, ∞). IP at (0, zero) H. part four. five precis OF CURVE SKETCHING 29. y = f (x) = ¤ √ three x2 − 1 A. D = R B. y-intercept: f (0) = −1; x-intercepts: f (x) = zero ⇔ x2 − 1 = zero ⇔ x = ±1 C. f (−x) = f (x), so the curve is symmetric concerning the y-axis. D. No asymptote E. f zero (x) = thirteen (x2 − 1)−2/3 (2x) = three three 2x . f zero (x) > zero ⇔ x > zero and f zero (x) < zero ⇔ x < zero, so f is (x2 − 1)2 expanding on (0, ∞) and reducing on (−∞, 0).

D) there's a aspect of inflection the place f adjustments from being CD to being CU, that's, at x = three. 33. (a) f (x) = 2x3 − 3x2 − 12x ⇒ f zero (x) = 6x2 − 6x − 12 = 6(x2 − x − 2) = 6(x − 2)(x + 1). f zero (x) > zero ⇔ x < −1 or x > 2 and f zero (x) < zero ⇔ −1 < x < 2. So f is expanding on (−∞, −1) and (2, ∞), and f is lowering on (−1, 2). (b) considering that f adjustments from expanding to lowering at x = −1, f (−1) = 7 is an area (d) greatest price. because f alterations from lowering to expanding at x = 2, f (2) = −20 is an area minimal price.

Y(30) = 100e30k = 12 (100) ⇒ e30k = ⇒ ok = −(ln 2)/30 ⇒ y(t) = 100e−(ln 2)t/30 = a hundred · 2−t/30 1 2 (b) y(100) = a hundred · 2−100/30 ≈ nine. ninety two mg 1 (c) 100e−(ln 2)t/30 = 1 ⇒ −(ln 2)t/30 = ln a hundred ⇒ t = −30 lnln0. 01 2 ≈ 199. three years eleven. enable y(t) be the extent of radioactivity. therefore, y(t) = y(0)e−kt and okay depends on utilizing the half-life: y(5730) = 12 y(0) ⇒ y(0)e−k(5730) = 12 y(0) ⇒ e−5730k = 1 2 ⇒ −5730k = ln 12 If seventy four% of the 14 C continues to be, then we all know that y(t) = zero. 74y(0) ⇒ zero. seventy four = e−t(ln 2)/5730 t=− ⇒ k=− ln 12 ln 2 = .