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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises use to determine whether the improper integral converges or diverges. 1 S 2/²ª x xp =
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim (1 + x)/x X-8
In Exercises use to determine whether the improper integral converges or diverges. 112 X dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim [3(x)/2] +0+x
In Exercises find the indefinite integral using any method. Sv √1 + √√x dx
In Exercises find the indefinite integral using any method. S 1 + cos x dx
Use mathematical induction to verify that the following integral converges for any positive integer n. ∞o xne-x dx
In Exercises find the indefinite integral using any method. x1/4 1 + x¹/2 dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim 1 + X
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim 1 + X
In Exercises find the indefinite integral using any method. csc √2x X dx
In Exercises determine all values of p for which the improper integral converges. 0 XP dx
In Exercises determine all values of p for which the improper integral converges. 8 1 XP dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim x¹/x X-8
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim (ex + x)²/xx x-0+
In Exercises find the indefinite integral using any method. S O sin cos e de
Verify the reduction formula tan" x dx 1 n - 1 tan"-¹ x S tan"-2 x dx.
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. ∞o 1 x ln x dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim x¹/x x-0+
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 8 4 √x(x + 6) dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim x tan x-00 1 X
Verify the reduction formula s (In x)" dx = x(In x)" - n -nf (In x)"-1 dx.
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). 1-1-) X limx sin x18
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 8 1 J3 X- ZX x√√√x² xp 6 - al
In Exercises use integration tables to find or evaluate the integral. 1 1+tan Tx dx
In Exercises use integration tables to find or evaluate the integral. 1 sin TX COS TTX dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim x³ cotx x-0+
In Exercises use integration tables to find or evaluate the integral. 3 2x√ √9x² - 1 dx, x > 3
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. *5 1 25 - x² dx
In Exercises use integration tables to find or evaluate the integral. X x² + 4x + 8 dx
In Exercises (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim x ln x X-∞0
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. *5 J3 1 √x²-9 dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x-1+ Ꮭ cos Ꮎ dᎾ x - 1
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 6 J3 1 36x² dx
In Exercises use integration tables to find or evaluate the integral. S X 1 + ex² dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim X-0 Siln(e4¹-1) dt X
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. *π/2 Jo sec Ꮎ dᎾ
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 2 x√x² - 4 1/2 x- dx
In Exercises use integration tables to find or evaluate the integral. S X /4+5x dx
In Exercises use integration tables to find or evaluate the integral. 0 π/2 X 1 + sin x² -dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. X lim x-o arctan 2x
In Exercises use integration tables to find or evaluate the integral. X (4 + 5x)2 dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x-0 arctan x sin x
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. So In x² dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 10 π/2 tan 0 de
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x→1 In x sin TX
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. So 10 x ln x dx
In Exercises use partial fractions to find the indefinite integral. x² x2 + 5x – 24 r2 dx
In Exercises use partial fractions to find the indefinite integral. sec²0 tan 0 (tan 0 - 1) dᎾ
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. ex/2 lim x-00 X
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. sin 5x lim x-0 tan 9x
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 8 3 8 - x dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. ex lim x-0014
In Exercises use partial fractions to find the indefinite integral. S 4x 2 3(x - 1)² dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. *5 10 - dx X Jo
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 2 1 =dx 3√x-1 So 10
In Exercises use partial fractions to find the indefinite integral. 5r – 2 x² X dx
In Exercises use partial fractions to find the indefinite integral. x³ x² + 2x x² + x - 1 dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. In x4 lim 3 x³ x-∞ X
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. 1 12 dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. sin x lim x-00 X-TT
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. In x lim xxx²
In Exercises find the indefinite integral using each method.(a) Trigonometric substitution(b) Substitution: u2 = 4 + x(c) Substitution: u = 4 + x(d) Integration by parts: √x √ 4 + x dx
In Exercises use partial fractions to find the indefinite integral. x - 39 x² - x - 12 dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. Sº sin X dx 2
In Exercises find the indefinite integral using each method.(a) Trigonometric substitution(b) Substitution: u2 = 4 + x2(c) Integration by parts: x3 √4 + x² dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x000 x2 x² + 1 뉴
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim ∞07x cos x X
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞o et 1 + et dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. Sº 0 COS TX dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim X-8 X L x² + 1
In Exercises use trigonometric substitution to find or evaluate the integral. So 0 6x³ 16+ x² dx
In Exercises use trigonometric substitution to find or evaluate the integral. [² 3 x³√√√x² - 9 dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x →∞0 x3 er
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞o x3 (x² + 1)² dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞o 0 1 et + ex dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. x3 lim x→∞ ex/2 X-
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞o 4 16 + x² dx
In Exercises use trigonometric substitution to find or evaluate the integral. 25 - 9x² dx
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞o In x - dx
In Exercises use trigonometric substitution to find or evaluate the integral. 4 + x² dx
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x →∞0 x³ x + 2
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 4 1 x(In x)³ dx
In Exercises use trigonometric substitution to find or evaluate the integral. S - 12 x²√ √4x² dx
In Exercises use trigonometric substitution to find or evaluate the integral. √√x²-9 X dx, x > 3
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x-x 5x+3 x² - 6x + 2
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim 007-x x² + 4x + 7 X-6
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 0 ex cos x dx
In Exercises find the area of the region. y = sin 3x cos 2x y 1 -1 (7:0) V. π 3 X
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim X-8 5x² + 3x1 4x² + 5
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. So x²e-x dx
In Exercises find the area of the region. y = sin4 x y R|4 RIN π X
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x→1 arctan x - (π/4) x - 1
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∞ -x/3 xe dx
In Exercises find the trigonometric integral. S cos 20(sin cos 0)² de
In Exercises find the trigonometric integral. 1 1 - sin Ꮎ dᎾ
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. sin ax lim x-o sin bx' where a, b 0
In Exercises evaluate the limit, using L’Hôpital’s Rule if necessary. lim x-0 arcsin x X
In Exercises determine whether the improper integral diverges or converges. Evaluate the integral if it converges. f xe-4x dx
In Exercises find the trigonometric integral. | X sec4 dx
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