Recent content by shuxue

An element of the domain of a real-valued function of a real variable is often called a point. For example, an element (point) ##p## in the domain of a real-valued function ##f## of a real variable where ##f'(p)=0## or ##f'(p)## is undefined is called a critical point of the function. The...

According to rules for working with approximate data, why the final result of a multiplication or division involving approximation data is round off so that the result has as many significant digits as the given data with the fewest significant digits? How is this rule established? For example...

What is meant by a precision of 23 bits (mantissa) in IEEE single precision format is equivalent to approximately 7 decimal digits precision?

Could someone please show me some examples how IEEE single precision format can used to store approximately 7 decimal digits of a number when the number is written in decimal format? How this is related to the statement ##2^{-23}=1.19\times10^{-7}##?

I want to solve the equation ##2 \sin^2\theta+2 \sin \theta-1=0##, ##0\leq\theta<2\pi##. By using the quadratic formula. I found one of the solution to be ##\theta=\sin^{-1}( \frac{-1+\sqrt{3}}{2})##. Which of the following ways of writing the numerical value of ##\theta## is correct? (i) or...

The example is taken from "Physics: For Scientists and Engineers", by Paul A. Tipler and Gene Mosca. I found another similar example in another textbook, "Fundamental of physics" by Halliday, Resnick, and Walker. The example is as follows: A pirate ship is 560 m from a fort defending a harbor...

The authors of a physics textbook want to determine the number of grains, N in a beach of 500 m long, 100 m wide, and 3 m deep. They assumed that each grain is 1-mm-diameter sphere. They also assumed that the grains are so tightly packed that the volume of the space between the grains is...