John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 7, 2023
Calculus

Evaluating the Limit of (tan(x) / sin(x)) as x Approaches 0: L’Hopital’s Rule and Rewriting in Terms of Sine and Cosine

Evaluate the limit Lim (tan(x)/sin(x))x→0 To evaluate the limit as x approaches 0 of (tan(x) / sin(x)), we can use L’Hopital’s Rule or rewrite the expression in...

John Rhodes
July 7, 2023
Calculus

Simplifying and evaluating the limit of (x² + x) / sin(x) as x approaches 0

Evaluate the limit Lim (x²+x)/(sin(x))x→0 To evaluate the given limit: lim (x² + x) / sin(x) as x approaches 0, we can try to simplify the expression...

John Rhodes
July 7, 2023
Calculus

Finding the Limit of (x²-1)/(x+2) as x Approaches 1: Step-by-Step Guide and Result

Evaluate the limit Lim (x²-1)/(x+2)x→1 To evaluate the limit of (x²-1)/(x+2) as x approaches 1, we can directly substitute the value of x into the expression and...

John Rhodes
July 7, 2023
Calculus

Understanding Polynomial Limits: When Does the Limit Approach Infinity?

True or FalseFor any polynomial p(x), Lim p(x) = ∞x→∞ The statement is false The statement is false. The notation “Lim p(x) = ∞ as x approaches...

John Rhodes
July 7, 2023
Calculus

Evaluating the Limit of (1 + (2/x))^2 as x Approaches Infinity: Step-by-Step Approach and Final Result

Evaluate the limit Lim (1 + (2/x))²x→∞ To evaluate the limit, we can first apply some algebraic manipulations to simplify the expression To evaluate the limit, we...

John Rhodes
July 7, 2023
Calculus

Evaluate the Limit of ln(2x)/x Using L’Hôpital’s Rule as x Approaches Infinity

Evaluate the limit Lim (ln2x)x→∞ To evaluate the limit of ln(2x)/x as x approaches infinity, we can use L’Hôpital’s rule To evaluate the limit of ln(2x)/x as...

John Rhodes
July 7, 2023
Calculus

Evaluating the Limit of (tan(x)/sec(x)) as x Approaches 0 using Trigonometric Simplifications

Evaluate the limit Lim Tan(x)/Sec(x)x→0 To evaluate the limit of (tan(x)/sec(x)) as x approaches 0, we can use the fact that tan(x) is equal to sin(x)/cos(x) and...

John Rhodes
July 7, 2023
Calculus

Evaluating the Limit of (x+2)/((√(x^2-4))) as x approaches 2

Evaluate the limit Lim (x+2)/((√x^2-4))x→2 To evaluate the limit, we can directly substitute the value of x=2 into the given expression and simplify: Lim (x+2)/((√(x^2-4))) as x...