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University of Toronto
MATH 101 — Calculus I
Midterm Examination
Time: 2 hours | Total: 80 marks
Section A: Multiple Choice (20 marks)
1. The limit of (sin x)/x as x approaches 0 is:
(a) 0 (b) 1 (c) ∞ (d) DNE
2. The derivative of ln(x²+1) is:
(a) 2x/(x²+1) (b) 1/(x²+1) ...
Section B: Short Answer (30 marks)
3. Evaluate the integral...
Solution Guide
MATH 101 — Calculus I
Section A: Multiple Choice
1. The limit of (sin x)/x as x approaches 0 is:
Answer: (b) 1
Apply L'Hopital's rule or use the squeeze theorem...
2. The derivative of ln(x²+1) is:
Answer: (a) 2x/(x²+1)
Apply chain rule: d/dx[ln(u)] = u'/u...
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