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Class 11 Limits and Derivatives worksheet
CBSE Mathematics. Standard limits, one-sided limits, derivatives from first principles and by rules. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
lim (x → 3) (3x² + x + 3) equals:
- −33
- 34
- 27
- 33
Answer
(d) 33
substitute directly
- 2.
lim (x → 4) (x⁶ − 4096) ÷ (x − 4) equals:
- 4,096
- 24,576
- 6,144
- 5,120
Answer
(c) 6,144
naⁿ⁻¹ = 6 × 4⁵
- 3.
lim (x → 0) (sin 2x ÷ sin 2x) equals:
- 2
- 3
- 0
- 1
Answer
(d) 1
use lim (sin θ)/θ = 1
Section B · short answer
- 4.
Evaluate lim (x → 3) (x² − 5x + 6) ÷ (x − 3).
Answer
1
factorise: (x − 3)(x − 2); cancel and put x = 3
- 5.
Evaluate lim (x → 3) (x³ − 27) ÷ (x − 3).
Answer
27
lim (xⁿ − aⁿ)/(x − a) = naⁿ⁻¹ = 3 × 3²
Section C · long answer
- 6.
Evaluate: (a) lim (x → 4) (x⁶ − 4,096) ÷ (x − 4); (b) lim (x → 0) (sin 3x) ÷ (sin 4x); (c) lim (x → −1) (x² − 1) ÷ (x + 1).
Answer
(a) 6,144; (b) 3/4; (c) −2
(c): x² − r² = (x − r)(x + r)
Fresh sheets for your child
In the app, every Limits and Derivatives sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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