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GRE Unit 1B1: Limit Concepts and Graphical Limits — practice questions — page 2

Explore 59 free Unit 1B1: Limit Concepts and Graphical Limits questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1B1: Limit Concepts and Graphical Limits questions and exercises with answers

Showing questions 31–59 of 59.

The product of two negative integers is:Read the answer and worked solution →Convert 3/4 to a decimal:Read the answer and worked solution →The product 22/7 × 7 equals:Read the answer and worked solution →Which expression is INCORRECT?Read the answer and worked solution →lim_(x→2) (x² - 4)/(x - 2) =Read the answer and worked solution →lim_(x→0) sin(x)/x =Read the answer and worked solution →For limit to EXIST at x = a, left-hand and right-hand limits must:Read the answer and worked solution →A function f is continuous at x = a if:Read the answer and worked solution →d/dx (xⁿ) = ?Read the answer and worked solution →lim_(x→0) (1 - cos x)/x² =Read the answer and worked solution →lim_(x→∞) (1 + 1/x)^x =Read the answer and worked solution →lim_(x→0) (e^x - 1)/x =Read the answer and worked solution →lim_(x→0) (sin 3x)/(sin 5x) =Read the answer and worked solution →d/dx (sin x) =Read the answer and worked solution →d/dx (eˣ) =Read the answer and worked solution →d/dx (ln x) =Read the answer and worked solution →Find d/dx (x² sin x) by product rule:Read the answer and worked solution →By chain rule, d/dx [sin(x²)] =Read the answer and worked solution →lim_(x→∞) (3x² - 5)/(7x² + 2) =Read the answer and worked solution →l'Hôpital's rule applies to limits of form:Read the answer and worked solution →Find dy/dx by implicit differentiation for x² + y² = 25:Read the answer and worked solution →d/dx (xˣ) where x > 0:Read the answer and worked solution →For f(x) = sin(1/x) for x ≠ 0, what is the limit as x → 0?Read the answer and worked solution →Differentiation by chain rule for d/dx [ln(sin x)]:Read the answer and worked solution →lim_(x→0) [(1 + x)^(1/x)] =Read the answer and worked solution →Higher-order derivative: d²/dx² (x⁴) =Read the answer and worked solution →f(x) is discontinuous at x = a if which condition fails?Read the answer and worked solution →For y = x³ - 6x² + 9x, find critical points (where y' = 0):Read the answer and worked solution →By Taylor expansion around x = 0: e^x = 1 + x + ___:Read the answer and worked solution →

Worked practice questions

The product of two negative integers is:

  1. Negative
  2. Positive
  3. Zero
  4. Cannot be determined
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Correct answer: B. Positive

**By Brahmagupta's rules:** negative × negative = positive. **Example:** (-3) × (-4) = +12. Conceptually: removing 4 debts of 3 each adds 12 to your fortune.

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Convert 3/4 to a decimal:

  1. 0.34
  2. 0.075
  3. 0.75
  4. 3.4
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Correct answer: C. 0.75

3 ÷ 4 = 0.75. The denominator 4 = 2² has only prime 2, so the decimal terminates. The decimal is 0.75 with 2 decimal places.

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The product 22/7 × 7 equals:

  1. 22 exactly
  2. An irrational number
  3. Approximately 21.99
  4. π
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Correct answer: A. 22 exactly

22/7 × 7 = 22 EXACTLY — basic arithmetic, no approximation. 22/7 is just a fraction. (Note: 22/7 ≈ π but is NOT π itself — π is irrational, 22/7 is rational. The chapter emphasises this distinction.)

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann Sums