John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 7, 2023
Calculus

Does f(2) Exist? Evaluating Statements Regarding the Existence of a Function Value at x=2.

Which of the following statements, if true, can be used to conclude that f(2) exists?i. limx→2f(x) exists.ii. f is continuous at x=2.iii. f is differentiable at x=2....

John Rhodes
July 7, 2023
Calculus

Calculating the Average Rate of Change of the Function f(x) = 1 + 3cos(x) Over the Interval [0, π]

The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π] ? To find the average rate of...

John Rhodes
July 7, 2023
Calculus

Calculating the Average Rate of Change of a Math Function over an Interval – Step by Step Guide and Example Solution

Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1,5] ? To...

John Rhodes
July 7, 2023
Calculus

Analyzing the Properties of the Function f(x)=(1/7)x^7+12x^6−x^5−(15/4)x^4+(4/3)x^3+6x^2: Determining Truth or Falsehood

Let f be the function given by f(x)=(1/7)x^7+12x^6−x^5−(15/4)x^4+(4/3)x^3+6x^2. Which of the following statements is true? To determine which of the following statements is true for the function...

John Rhodes
July 7, 2023
Calculus

Calculating the Difference between Approximation and Actual Value of f′(0.5) for the Function f(x) = 2x^3

Let f be the function given by f(x)=2×3. Selected values of f are given in the table above. If the values in the table are used to...

John Rhodes
July 7, 2023
Geometry

Understanding Alternate Exterior Angles and Their Congruency in Geometry

alternate exterior angles are congruent Alternate exterior angles are pairs of angles that are formed when a transversal intersects two parallel lines Alternate exterior angles are pairs...

John Rhodes
July 7, 2023
Geometry

Proving the Congruence of Corresponding Angles in Parallel Lines and Transversals

if 2 parallel lines are cut by transversals, then corresponding angles are congruent To prove that corresponding angles formed by the intersection of two parallel lines and...

John Rhodes
July 7, 2023
Geometry

Understanding the Congruence of Complementary Angles: Exploring the Relationship Between Angle Measures

complements of congruent angles are congruent To understand why the complements of congruent angles are congruent, we need to first establish some basic definitions To understand why...