Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Step-by-Step Guide to Finding the Derivative of Cot(x) using Quotient Rule in Mathematics

d/dx(cotx) csc²x To find the derivative of cot(x), we can use the quotient rule: Let u = cos(x) and v = sin(x): cot(x) = cos(x) / sin(x)...

John Rhodes
June 21, 2023
Calculus

Understanding Limits in Calculus: Defining Limits with Epsilon-Delta Notation

Limit definition As x approaches c, (number/constant), as the values of x get arbitrarily close to c, the values of f(x) approach L, the limit (Y value...

John Rhodes
June 21, 2023
Calculus

Understanding Limits in Mathematics: Requirements for Existence and Consistency

In order for a limit to exist, what must happen? The values of f must tend to the same number L, as x approaches from either left...

John Rhodes
June 21, 2023
Calculus

Understanding Infinite Limits in Calculus: Exploring the Behavior of Functions Near Certain Points.

Infinite limits Infinite limit if as x approaches c if f(x) can be made arbitrarily large by taking x sufficiently close to c (exponentially increasing)Can be positive...

John Rhodes
June 21, 2023
Calculus

Mastering Horizontal Asymptotes in Rational Functions: A Guide to the Three Essential Rules

Three rules of horizontal asymptotes When the top degree is less than the bottom degree the asymptote is the x axisWhen they are the same degrees, divide...

John Rhodes
June 21, 2023
Calculus

Understanding Vertical Asymptotes in Mathematics: Definition, Examples, and Significance

Vertical Asmptote If one side of the limit approaches infinity usually in 1/x kind of functions, rational functionsin 1/(1-x) x=1 would be a VA In mathematics, a...

John Rhodes
June 21, 2023
Calculus

Squeeze Theorem: Simplify Limits of Functions with Sandwich Approach – A Guide to Using the Squeeze Theorem in Calculus

Squeeze or Sandwich Theorem The squeeze (or sandwich) theorem states that if f(x)≤g(x)≤h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must...

John Rhodes
June 21, 2023
Calculus

Discover the Math Behind The Equivalent of 1/Infinity to Zero

1/infinity 0 The expression 1/infinity is equivalent to zero. Mathematically, we can represent infinity using the symbol ∞. When we divide any number by ∞, the result...