Free Printable Newton & Lebniz

1.

Newton provide an example of power series in which book?

a)

Treatise

b)

Clavis mathematicae

c)

Arithmetica infinitorum

d)

Deanalysi

2.

Newton’s discovery of power series came out of his reading of (a)

3.

Find $d(\log\sqrt{(}x^2+y^2))$

a)

$(xdx-ydy)/(x^2+y^2)$

b)

$(xdx+ydy)/(x^2-y^2)$

c)

$(xdx-ydy)/(x^2-y^2)$

d)

$(xdx+ydy)/(x^2+y^2)$

4.

When did Newton send his second (and last) letter to Leibniz?

a)

October 24, 1675

b)

October 24, 1676

c)

October 24, 1677

d)

October 24, 1678

5.

Newton served two brief terms as Member of Parliament of the University of Cambridge. When were these two terms?

a)

1688-1690 and 1701-1702

b)

1689-1690 and 1701-1703

c)

1689-1690 and 1700-1701

d)

1689-1690 and 1701-1702

6.

Give the equation

$2x^4-ax^2y+2axy^2-y^4=0$

Find $ẋ∶ẏ$

a)

$ẋ∶ẏ=(8x^3-2axy+2ay^2)∶(ax^2-4axy+4y^3)$

b)

$ẋ∶ẏ=(-ax^2+4axy-4y^3)∶(8x^3-2axy+2ay^2)$

c)

$ẋ∶ẏ=(ax^2-4axy+4y^3)∶(8x^3-2axy+2ay^2)$

d)

$ẋ∶ẏ=(8x^3-2axy+2ay^2)∶(-ax^2+4axy-4y^3)$

7.

By Leibniz, what is the expression for ? $\pi/4$

a)

$\pi/4=1-1/3+1/5-1/7+⋯$

b)

$\pi/4=1-1/2+1/4-1/6+⋯$

c)

$\pi/4=1+1/3+1/5+1/7+⋯$

d)

$\pi/4=1+1/2+1/4+1/6+⋯$

8.

By applying Leibniz’s formula, find the sum of $1/4+1/20+1/60+1/140+⋯$

a)

2/15

b)

1/3

c)

1/20

d)

34/105

9.

Between Isaac Newton and Leibniz, who was the person having the interest in differential first, and who was the person publishing the discovery of differential calculus first?

a)

Leibniz – Leibniz

b)

Newton – Newton

c)

Newton – Leibniz

d)

Leibniz – Newton

10.

Arrange the step to find the fluent given the fluxion into the correct order according to the 1^st method.

(1) Dividing by and then by the number of dimensions.

(2) Carrying out the same operation in the terms multiplied by .

(3) Arranging the terms multiplied by according to the dimensions of .

(4) Setting the total of the resulting terms equal to nothing.

(5) Reject redundant terms.

a)

(3)(1)(5)(2)(4)

b)

(3)(1)(2)(5)(4)

c)

(3)(5)(1)(4)(2)

d)

(3)(5)(1)(2)(4)

Newton & Lebniz

Total questions: 10

Worksheet time: 6mins

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