Author Archives: fangxiao zhang

First Order Differential Equations Differential equation is a type of equations that contain both a function f and its derivative. First order means that the highest order of differentiation is one. For example, second derivative should not appear in the … Continue reading →

Definition of analytic function – A function is analytic at c means that the Taylor series of the function converges to itself at point c.  In other words, at a point c, there exists a series that exactly equals to the … Continue reading →

As for this midterm, the relatively difficult question for me was number 3. This question was not hard, but I was confused by the function inside the integral. Although I knew the fundamental theorem of calculus was the key to … Continue reading →

The goal of using substitutions is to simplify the integral. A good substituion can solve it faster. Generally, we want to reduce the power or simplify into a ploynomial. Here are some tips on how to make a substitution in … Continue reading →

Functions with finitely many removable discontinuities are integrable. Let f(x) be a defined function on [a, b]. This function has N removable discontinuity, where N is a finite positive integer. We partition [a, b] into n subintervals of width (b-a)/n. … Continue reading →

f(x)=x2ln(x) What is the domain of the function? Does this function have any intercepts with the axis? What are the turning points? What is the x value of the point of inflection? Sketch the graph.

A person flies a kite on the main mall. The kite rises at a rate of 2 meters per second. Suppose the horizontal distance between the person and the kite is always 6m, how fast must he release the string when … Continue reading →

First of all, we need to understand that the function of the temperature is continuous. In other words, the temperature changes gradually, either increasing or decreasing. It’s impossible for a 100 degree Celsius object become 0 degree Celsius at the … Continue reading →

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The distance of walking can be represented by a function. Suppose a person is walking at a constant speed, then the growth rate of the distance he travels is a constant number. Since the displacement per unit time are all the … Continue reading →