By Isaac Todhunter

This Elibron Classics e-book is a facsimile reprint of a 1864 variation via Macmillan and Co., Cambridge and London.

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**Additional resources for A Treatise On The Differential Calculus with numerous examples**

**Example text**

In general terms, if a is a positive real number, then the square root of a is a number that, when multiplied by itself, gives a. The square root could be positive or negative because multiplying two negative numbers gives a positive number. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root obtained using a calculator is the principal square root. — The principal square root of a is written as √ a . The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression.

30 CHAPTER 1 Prerequisites 48. 71496 × 1013. Rewrite the GDP in standard notation. 49. 397 × 10−11 in. Rewrite this length using standard notation. 50. S. 6 billion. Rewrite this amount in scientific notation. TECHNOLOGY For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth. 2 12 m 51. ______ 3 33 4−3 52. 173 ÷ 152x3 EXTENSIONS For the following exercises, simplify the given expression. Write answers with positive exponents. 32 a3 −2 a4 22 2 53.

91 × 10−7 d. 05 × 10−12 Solution a. 54700000000000 → 14 places 354,700,000,000,000 b. 000000 → 6 places −2,000,000 c. 000000791 d. 2 Exponents and Scientific Notation Try It #11 Convert each number in scientific notation to standard notation. 03 × 105 b. 16 × 1011 c. 8 × 10−6 Using Scientific Notation in Applications Scientific notation, used with the rules of exponents, makes calculating with large or small numbers much easier than doing so using standard notation. For example, suppose we are asked to calculate the number of atoms in 1 L of water.

### A Treatise On The Differential Calculus with numerous examples by Isaac Todhunter

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