John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 30, 2023
Calculus

Determining the Value of k for a Continuous Piecewise Function

determine the value of k so that the piecewise function below is continuous.f(x)={kx−1 k+5x. if x≤3 if x>3 To determine the value of k for the piecewise...

John Rhodes
July 30, 2023
Calculus

Determining the Minimum Number of Zeros of a Function Using the Intermediate Value Theorem | An Analysis of Behavior and Sign Changes

The function f(x) is continuous on the interval [1,10]. The table below gives some of its values. What is the minimum number of zeros that f(x) is...

John Rhodes
July 30, 2023
Calculus

Determining the Limit of a Piecewise Function as x Approaches -4 | Left-hand and Right-hand Limits Analysis

Given the following piecewise function, evaluate limx→−4+f(x).f(x)=−2×2−x−32x^2+x+32×2−2if x−2 To evaluate the limit limx→−4+f(x) of the given piecewise function, we need to determine the value of f(x) as...

John Rhodes
July 30, 2023
Calculus

Evaluating the Limit of (f(x) – 4g(x)) at x = -2 | A Step-by-Step Guide

Given that limx→−2 of f(x)=−4 and limx→−2 of g(x)=5, evaluate the following.limx→−2 of (f(x)−4g(x)) To evaluate the limit limx→−2 of (f(x) – 4g(x)), we can make use...

John Rhodes
July 30, 2023
Calculus

The Limit as x Approaches 0 of |4x-1|-|4x+1|/x | Left and Right-Hand Limits Analysis

compute: limit as x approaches 0 (|4x-1|-|4x+1|)/x) To compute the limit as x approaches 0 of the expression |4x-1|-|4x+1| divided by x, we’ll consider the left and...

John Rhodes
July 30, 2023
Calculus

Simplifying and Finding the Limit of an Expression as x Approaches 9

Find the following limit.limx→9 of x−9/sq root of (x-3)-sq root of 6 To find the limit of this expression as x approaches 9, we will start by...

John Rhodes
July 30, 2023
Calculus

Evaluating the Limit as x Approaches 0 | (x^2)/(x+6) + (36/(x-6)) Simplified

Evaluate the limit.limx→0 x^2/x+6+(36/x−6) To evaluate the limit as x approaches 0 for the expression (x^2)/(x+6) + (36/(x-6)), we can simplify the expression first and then substitute...

John Rhodes
July 30, 2023
Calculus

Using L’Hôpital’s Rule to Evaluate the Limit of (7x)/(sin(3x)) as x Approaches 0

Evaluate the limit below.limx→0 7x/sin(3x) To evaluate the limit of the function (7x)/(sin(3x)) as x approaches 0, we can use L’Hôpital’s Rule To evaluate the limit of...