John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

How To Differentiate Cot(X) With Respect To X Using The Quotient Rule Of Differentiation

d/dx (cotx)= (-cscx)∧2 To differentiate cot(x) with respect to x, we can rewrite the expression as cos(x)/sin(x). Using the quotient rule of differentiation, d/dx [cos(x)/sin(x)] = (sin(x)(-sin(x))...

John Rhodes
June 21, 2023
Calculus

Mastering The Chain Rule Of Differentiation For Sec X: Derivative Simplified

d/dx (secx)= secx×tanx Using the chain rule of differentiation, we can find the derivative of sec x with respect to x as follows: Let y = sec...

John Rhodes
June 21, 2023
Calculus

Continuity In Math: Definition And Examples

Definition of Continuity:1) ___________________2) ___________________3) ___________________ 1) f(c) is defined2) lim x->c of f(c) exits3) lim x-> c of f(x) = f(c) 1) Continuity is a property...

John Rhodes
June 21, 2023
Calculus

The Intermediate Value Theorem: Using Continuity To Find Solutions And Roots.

Intermediate Value Theorem:1) ___________________2) ___________________3) ___________________ then there exits a number c between a and b for which f(c) = k 1) f(x) is continues on [a,b]2)...

John Rhodes
June 21, 2023
Calculus

Derivatives: A Comprehensive Guide To Calculus And Its Real-World Applications.

Definition of the Derivativef'(x) = ___________________ lim h->0 f(x+h)-f(x) / h The derivative of a function f(x) at a point x is defined as the instantaneous rate...

John Rhodes
June 21, 2023
Calculus

The Alternative Definition Of The Derivative In Calculus

Alternative form of the definition of the derivative lim x->c. f(x)-f(c) / x-c One alternative form of the definition of the derivative of a function is: The...

John Rhodes
June 21, 2023
Calculus

Why The Limit Of Sin(Theta)/Theta As Theta Approaches 0 Is Equal To 1: A Visual Explanation Using The Unit Circle

lim theta->0 sin(theta) / theta = ___________________ 1 The limit of sin(theta)/theta as theta approaches 0 is equal to 1. To see why, consider the unit circle...

John Rhodes
June 21, 2023
Calculus

How To Evaluate The Limit Using L’Hopital’S Rule And Small-Angle Approximation In Mathematics

lim theta->0 1 – cos(theta) / theta = ___________________ 0 To evaluate this limit, we can use L’Hopital’s rule or the small-angle approximation. Using L’Hopital’s rule: We...