EMA1501 Assignment 5 Complete Answers Study Guide
2025/2026 || Verified Solutions and Correct Explanations
Description:
EMA1501 Assignment 5 complete study resource for 2025/2026. Provides accurate
solutions covering engineering mathematics with step-by-step verified answers.
Keywords:
EMA1501 assignment 5 answers
engineering mathematics prep
EMA1501 complete solutions
EMA1501 verified answers 2025
math exam study guide
Part 1: Calculus I - Limits and Continuity
1. Question: Evaluate the limit: lim (x→2) (x² - 4)/(x - 2)
Answer: Factor the numerator: (x-2)(x+2)/(x-2). Simplify to x+2. Substituting x=2 gives 4.
2. Question: What is lim (x→0) sin(x)/x?
Answer: This is a standard limit. The result is 1.
3. Question: Determine the limit: lim (x→∞) (3x² + 2x - 1) / (5x² - x + 7)
Answer: Divide numerator and denominator by x². This gives (3 + 2/x - 1/x²) / (5 - 1/x + 7/x²).
As x→∞, terms with x in the denominator go to 0. The limit is 3/5.
, 4. Question: Is the function f(x) = |x| continuous at x=0? Explain.
Answer: Yes, it is continuous. The limit as x→0 exists and is equal to the function's value at
x=0, which is 0.
5. Question: Find lim (x→3) (1/x - 1/3) / (x - 3)
Answer: Combine terms in the numerator: (3 - x)/(3x) / (x-3) = (3 - x)/(3x(x-3)) = -1/(3x).
Substituting x=3 gives -1/9.
Part 2: Calculus I - Differentiation (Basics)
6. Question: Using the first principles, find the derivative of f(x) = x².
Answer: f'(x) = lim (h→0) [( (x+h)² - x² ) / h] = lim (h→0) [ (x²+2xh+h² - x²) / h ] = lim (h→0) [
(2xh + h²) / h ] = lim (h→0) [2x + h] = 2x.
7. Question: What is the derivative of f(x) = 5?
Answer: The derivative of any constant is 0.
8. Question: Differentiate y = 4x³ - 3x² + 2x - 5.
Answer: Applying the power rule: dy/dx = 12x² - 6x + 2.
9. Question: Find the derivative of f(x) = √x.
Answer: Rewrite as x^(1/2). Using the power rule: f'(x) = (1/2)x^(-1/2) = 1/(2√x).
10. Question: What is the derivative of sin(x)?
Answer: cos(x).
Part 3: Calculus I - Differentiation (Rules)
2025/2026 || Verified Solutions and Correct Explanations
Description:
EMA1501 Assignment 5 complete study resource for 2025/2026. Provides accurate
solutions covering engineering mathematics with step-by-step verified answers.
Keywords:
EMA1501 assignment 5 answers
engineering mathematics prep
EMA1501 complete solutions
EMA1501 verified answers 2025
math exam study guide
Part 1: Calculus I - Limits and Continuity
1. Question: Evaluate the limit: lim (x→2) (x² - 4)/(x - 2)
Answer: Factor the numerator: (x-2)(x+2)/(x-2). Simplify to x+2. Substituting x=2 gives 4.
2. Question: What is lim (x→0) sin(x)/x?
Answer: This is a standard limit. The result is 1.
3. Question: Determine the limit: lim (x→∞) (3x² + 2x - 1) / (5x² - x + 7)
Answer: Divide numerator and denominator by x². This gives (3 + 2/x - 1/x²) / (5 - 1/x + 7/x²).
As x→∞, terms with x in the denominator go to 0. The limit is 3/5.
, 4. Question: Is the function f(x) = |x| continuous at x=0? Explain.
Answer: Yes, it is continuous. The limit as x→0 exists and is equal to the function's value at
x=0, which is 0.
5. Question: Find lim (x→3) (1/x - 1/3) / (x - 3)
Answer: Combine terms in the numerator: (3 - x)/(3x) / (x-3) = (3 - x)/(3x(x-3)) = -1/(3x).
Substituting x=3 gives -1/9.
Part 2: Calculus I - Differentiation (Basics)
6. Question: Using the first principles, find the derivative of f(x) = x².
Answer: f'(x) = lim (h→0) [( (x+h)² - x² ) / h] = lim (h→0) [ (x²+2xh+h² - x²) / h ] = lim (h→0) [
(2xh + h²) / h ] = lim (h→0) [2x + h] = 2x.
7. Question: What is the derivative of f(x) = 5?
Answer: The derivative of any constant is 0.
8. Question: Differentiate y = 4x³ - 3x² + 2x - 5.
Answer: Applying the power rule: dy/dx = 12x² - 6x + 2.
9. Question: Find the derivative of f(x) = √x.
Answer: Rewrite as x^(1/2). Using the power rule: f'(x) = (1/2)x^(-1/2) = 1/(2√x).
10. Question: What is the derivative of sin(x)?
Answer: cos(x).
Part 3: Calculus I - Differentiation (Rules)
