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51. lim x→1 2. / 1 53. lim x-0+ X 1 55. lim - X 1 x→0+ X X - 57. lim x√x x-0+ 63. lim x¹/x x18 - 1 1 tan x 59. lim (1-2x)¹/x x->0 61. lim x¹/(1-x) x-1+ 1 e* - 1 In x 65. lim (4x + 1) cotx x->0+ 52. lim (csc x x-0 54. lim x→0+ 1 X - 64. lim x 818 - 56. lim (x In x) 818 dl od (018 15. 60. lim 1 + 818 cot x) 1 tan ¹x 58. lim (tan 2x)* x-0+ X bx 62. lim (e* + 10x)¹/x x18 66. lim (1 cos x) sin x x-0+

51. lim x→1 2. / 1 53. lim x-0+ X 1 55. lim - X 1 x→0+ X X - 57. lim x√x x-0+ 63. lim x¹/x x18 - 1 1 tan x 59. lim (1-2x)¹/x x->0 61. lim x¹/(1-x) x-1+ 1 e* - 1 In x 65. lim (4x + 1) cotx x->0+ 52. lim (csc x x-0 54. lim x→0+ 1 X - 64. lim x 818 - 56. lim (x In x) 818 dl od (018 15. 60. lim 1 + 818 cot x) 1 tan ¹x 58. lim (tan 2x)* x-0+ X bx 62. lim (e* + 10x)¹/x x18 66. lim (1 cos x) sin x x-0+

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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57,59,63
### Calculus: Limits Practice Problems Here are a series of limit problems commonly encountered in calculus classes. These problems are designed to help students practice and master the concept of limits. 51. \(\lim_{{x \to 1}} \left( \frac{x}{{x - 1}} - \frac{1}{{\ln x}} \right)\) 52. \(\lim_{{x \to 0}} (\csc x - \cot x)\) 53. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{e^x - 1}} \right)\) 54. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{\tan^{-1} x}} \right)\) 55. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{\tan x}} \right)\) 56. \(\lim_{{x \to \infty}} (x - \ln x)\) 57. \(\lim_{{x \to 0^+}} x^{x/x}\) 58. \(\lim_{{x \to 0^+}} (\tan 2x)^x\) 59. \(\lim_{{x \to 0}} (1 - 2x)^{1/x}\) 60. \(\lim_{{x \to \infty}} \left( 1 + \frac{a}{x} \right)^{bx}\) 61. \(\lim_{{x \to 1^+}} x^{1/(1-x)}\) 62. \(\lim_{{x \to \infty}} (e^x + 10x)^{1/x}\) 63. \(\lim_{{x \to \infty}} x^{1/x}\) 64. \(\lim_{{x \to \infty}} x e^{-x}\) 65. \(\lim_{{x \to 0^+}} (4x + 1)^{\cot x}\) 66. \(\lim_{{x \to 0^+}} (1 - \cos x)^{\sin x}\)
Transcribed Image Text:### Calculus: Limits Practice Problems Here are a series of limit problems commonly encountered in calculus classes. These problems are designed to help students practice and master the concept of limits. 51. \(\lim_{{x \to 1}} \left( \frac{x}{{x - 1}} - \frac{1}{{\ln x}} \right)\) 52. \(\lim_{{x \to 0}} (\csc x - \cot x)\) 53. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{e^x - 1}} \right)\) 54. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{\tan^{-1} x}} \right)\) 55. \(\lim_{{x \to 0^+}} \left( \frac{1}{x} - \frac{1}{{\tan x}} \right)\) 56. \(\lim_{{x \to \infty}} (x - \ln x)\) 57. \(\lim_{{x \to 0^+}} x^{x/x}\) 58. \(\lim_{{x \to 0^+}} (\tan 2x)^x\) 59. \(\lim_{{x \to 0}} (1 - 2x)^{1/x}\) 60. \(\lim_{{x \to \infty}} \left( 1 + \frac{a}{x} \right)^{bx}\) 61. \(\lim_{{x \to 1^+}} x^{1/(1-x)}\) 62. \(\lim_{{x \to \infty}} (e^x + 10x)^{1/x}\) 63. \(\lim_{{x \to \infty}} x^{1/x}\) 64. \(\lim_{{x \to \infty}} x e^{-x}\) 65. \(\lim_{{x \to 0^+}} (4x + 1)^{\cot x}\) 66. \(\lim_{{x \to 0^+}} (1 - \cos x)^{\sin x}\)
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