Class 11 Mathematics · Chapter 13 · Test 1
Derivative from First Principle
40 MCQs Covers the definition of the derivative, notations, first-principle derivatives, gradient and tangent equations (Ex 13.1).
40 questions · 35 min · 40 marks
Want to try first? Take the free Mathematics test: Complex Number Operations
Sample questions
The first 5 of 40. Try each one, then tap to see the answer.
Question 1
The derivative of f(x) by first principle is defined as
- Alim(h→0) [f(x+h) + f(x)] / h
- Blim(h→0) [f(x+h) − f(x)] / h
- Clim(h→0) [f(x) − f(x+h)] / h
- Dlim(h→∞) [f(x+h) − f(x)] / h
Show answerHide answer
Answer: B
f′(x) = lim(h→0) [f(x+h) − f(x)]/h, the limit of the difference quotient.
Question 2
In the delta method, the increment δy corresponding to δx is
- Af(x + δx) + f(x)
- Bf(x) − f(x − δx) + δx
- Cf(x + δx) ÷ f(x)
- Df(x + δx) − f(x)
Show answerHide answer
Answer: D
δy = f(x+δx) − f(x), and dy/dx = lim(δx→0) δy/δx.
Question 3
The notation dy/dx for the derivative is due to
- ALeibniz
- BNewton
- CLagrange
- DCauchy
Show answerHide answer
Answer: A
dy/dx is Leibniz's notation.
Question 4
The dot notation ẏ for the derivative with respect to time is due to
- ALeibniz
- BLagrange
- CNewton
- DCauchy
Show answerHide answer
Answer: C
Newton's notation puts a dot over the variable.
Question 5
The prime notation f′(x) for the derivative is due to
- ANewton
- BLagrange
- CLeibniz
- DCauchy
Show answerHide answer
Answer: B
f′(x) is Lagrange's notation.
More tests in Differentiation
Practise with a free account
Save your scores, see which chapters need work, and keep a notebook of every question you got wrong.