# Limits at Infinity

Home > Differentiation We can use the knowledge of limits to explore of functions for extreme values of $x$, which is the limits of infinity. $x \rightarrow \infty$ to mean when $x$ gets as large as we like and positive, $x \rightarrow -\infty$ to mean when $x$ gets as large as we like and negative. [...]

# Definition of Limits

Home > Differentiation The concept of a limit is essential to differential calculus. We will see that calculating limits is necessary for finding the gradient of a tangent to a curve at any point on the curve. Consider the following table of values for $f(x)=x^2$ where $x$ is less than $3$ but increasing and getting [...]

# Rates of Change

Conceptual Understanding of Rates of Change A rate is a comparison between two quantities with different units. We often judge performances by using rates. For example: Average speed of a motor vehicle is $90$ km per hour. Average typing rate is $55$ words per minute. Average score of a basketball player is $34$ points per […]

# 5 Important Patterns of First Principles

Share0 Share +10 Tweet0 First Principles The First Principles defines how basic rule of derivative of a function. $$\displaystyle f'(x) = \lim_{h\to\infty} \frac{f(x+h)-f(x)}{h}$$ Patterns of the First Principles Pattern 1 Differentiate $f(x) = x^2$ from the first principles. Pattern 2 Differentiate $f(x) = x^3$ from the first principles. Pattern 3 Differentiate […]

# Finding a Function from Differential Equation

Share0 Share +10 Tweet0 The solution of a differential equation is to find an expression without $\displaystyle \frac{d}{dx}$ notations using given conditions. Note that the proper rules must be in place in order to achieve the valid solution of the differential equations, such as product rule, quotient rule and chain rule particularly. Many students […]