Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Intermediate Value Theorem: Calculus Concepts and Proving Real Roots in Functions.

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

the Derivative in Calculus: Definition, Formula, and 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 gives the instantaneous rate of change...

John Rhodes
June 21, 2023
Calculus

Mastering Calculus: the Alternative Definition of Derivatives

Alternative form of the definition of the derivative lim x->c. f(x)-f(c) / x-c The derivative of a function f(x) at a point x=a can also be defined...

John Rhodes
June 21, 2023
Calculus

Proving the Well-Known Limit of Sin(theta)/theta as Theta Approaches 0 = 1 Using Squeeze Theorem and L’Hopital’s Rule

lim theta->0 sin(theta) / theta = ___________________ 1 The limit of sin(theta) / theta as theta approaches 0 is equal to 1. This is a well-known limit...

John Rhodes
June 21, 2023
Calculus

Learn how to evaluate the limit of (1-cos(theta))/theta using L’Hopital’s rule

lim theta->0 1 – cos(theta) / theta = ___________________ 0 To evaluate the limit: lim theta->0 (1 – cos(theta)) / theta We can use L’Hopital’s rule which...

John Rhodes
June 21, 2023
Calculus

Master the Power Rule: How to easily calculate derivatives of x^n with examples

Power Rule:d/dx [x^n] = ___________________ nx^n-1 The power rule states that the derivative of x raised to the power of n, denoted as x^n, is equal to...

John Rhodes
June 21, 2023
Calculus

Calculus: Why the Derivative of a Constant is Always 0

derivative of a constant:d/dx [c] = ___________________ 0 The derivative of a constant is always 0. This is because the derivative measures the rate of change of...

John Rhodes
June 21, 2023
Calculus

Sum and Difference Rules of Differentiation in Mathematics

Sums and Differences:1) d/dx [f(x) + g(x)] = ___________________2) d/dx [f(x) – g(x)] = ___________________ 1) f'(x) + g'(x)2) f'(x) – g'(x) 1) According to the sum...