John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Limits: Behavior Of Functions As X Approaches Infinity

limits as x approaches infinity horizontal asymptotes When we say limits as x approaches infinity, we are essentially asking the question: What value does the function approach...

John Rhodes
June 21, 2023
Calculus

Mastering Limits: A Step-By-Step Guide For Evaluating Limits With Expressions Involving X

lim x->∞ pow top < pow bottom 0 If we have a limit of the form: lim x->∞ pow top < pow bottom, where pow top and...

John Rhodes
June 21, 2023
Calculus

Applying L’Hopital’S Rule: How To Solve Indeterminate Limits With Derivatives

lim x->∞ pow top = pow bottom coefficients In order to solve this limit problem, we can use L’Hopital’s Rule, which states that if we have an...

John Rhodes
June 21, 2023
Calculus

Guide To Evaluating Limits Of Functions Using Exponents At Infinity For Positive Integers A And B

lim x->∞ pow top > pow bottom ∞, -∞ To evaluate this limit, we need to consider the behavior of the top and bottom functions as x...

John Rhodes
June 21, 2023
Calculus

Mastering Continuity In Calculus: The Importance And Definition

Continuity lim x->C = lim x->C+ = lim x->C- = f(c) In calculus, continuity refers to the property of a function having no holes, gaps or jumps...

John Rhodes
June 21, 2023
Calculus

Discontinuity In Mathematics: Types And Significance.

Discontinuity jump, hole/removable, ∞, oscillating Discontinuity in mathematics refers to a point where a function does not exist or exhibits a peculiar behavior at a certain value...

John Rhodes
June 21, 2023
Calculus

Unlocking The Power Of Calculus: The Intermediate Value Theorem For Root-Finding And Beyond

Intermediate Value Theorem (IVT) If f(x) is continuous on the closed interval [a,b], then f(x) will take on every value between f(a) and f(b) The Intermediate Value...

John Rhodes
June 21, 2023
Calculus

The Power Of Constant Functions: Definition, Graphs, And Practical Applications

Constant function f(x) = b A constant function is a type of mathematical function that always produces the same output for every input. In other words, it...