Carson Merrill

Pepperdine University

Biography

I am a Mathematics Education student from Pepperdine University. I have over five years of experience in tutoring students of all ages and backgrounds. I have a strong passion for math, and I look forward to helping any student who is willing and ready to learn!

Education

BA Mathematics Education

Pepperdine University

BS Mechanical Engineering

California Baptist University

Topics Covered

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Derivatives

Differentiation

Trigonometry

Circles

Graphs and Statistics

Functions

Graph Linear Functions

Right Triangles

Congruent Triangles

Relationships Within Triangles

Fractions and Mixed Numbers

Decimals

Functions

Polynomials

Rational Functions

Linear Functions

Introduction to Conic Sections

The Integers

Equations and Inequalities

Quadratic Functions

Exponents and Polynomials

Exponential and Logarithmic Functions

Functions

Limits

Functions of Several Variables

Systems of Equations and Inequalities

Continuous Functions

Applications of the Derivative

Differential Equations

Parametric Equations

Volume

Introduction to Matrices

Polar Coordinates

Vectors

Lines and Planes in Space

Complex Numbers

Integrals

Applications of Integration

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

Integration Techniques

Improper Integrals

Introduction to Trigonometry

Matrices

An Introduction to Geometry

Introduction to Vectors

Series

Introduction to Combinatorics and Probability

Integration

Series Tests

Foundations for Geometry

Geometry Basics

Probability

Sequences

Area Between Curves

Arc Length and Surface Area

Power Series

Taylor Series

The Dot Product

The Cross Product

Second-Order Differential Equations

Integration Review

Descriptive Statistics

Linear Regression and Correlation

Sampling and Data

Frequency Distributions and Graphs

Testing the Difference Between Two Means, Two Proportions, and Two Variances

The Normal Distribution

The Real Economy in the Long Run

Introduction to Sequences and Series

The Normal Distribution

Discrete Random Variables

Probability Topics

Sampling and Simulation

Hypothesis Testing with One Sample

Angles

The Chi-Square Distribution

Continuous Random Variables

Applications of Trigonometric Functions

Graphing Trigonometry Functions

The Central limit Theorem

Hypothesis Testing with Two Samples

Hypothesis Testing

The Language of Algebra

Rational Numbers

Linear Equations and Inequalities

Trig Integrals

Carson's Textbook Answer Videos

01:08

Calculus: Early Transcendentals

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) $ y = \pi^x $
(b) $ y = x^\pi $
(c) $ y = x^2 (2 - x^3) $
(d) $ y = \tan t - \cos t $
(e) $ y = \frac{s}{1 + s} $
(f) $ y = \frac{\sqrt {x^3 - 1}}{1 + \sqrt[3]{x}} $

Chapter 1: Functions and Models

Section 2: Mathematical Models: A Catalog of Essential Functions

01:06

Calculus: Early Transcendentals

The point $ P(2, -1) $ lies on the curve $ y = 1/(1-x) $.

(a) If $ Q $ is the point $ (x, 1/(1-x)) $, use your calculator to find the slope of the secant line $ PQ $ (correct to six decimal places) for the following values of $ x $:
(i) $ 1.5 $ (ii) $ 1.9 $ (iii) $ 1.99 $ (iv) $ 1.999 $
(v) $ 2.5 $ (vi) $ 2.1 $ (vii) $ 2.01 $ (viii) $ 2.001 $

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at $ P(2, -1) $.

Chapter 2: Limits and Derivatives

Section 1: The Tangent and Velocity Problems

01:13

Calculus: Early Transcendentals

The point $ P(0.5, 0) $ lies on the curve $ y = \cos \pi x $.

(a) If $ Q $ is the point $ (x, \cos \pi x) $, use your calculator to find the slope of the secant line $ PQ $ (correct to six decimal places) for the following values of $ x $:

(i) $ 0 $ (ii) $ 0.4 $ (iii) $ 0.49 $
(iv) $ 0.499 $ (v) $ 1 $ (vi) $ 0.6 $
(vii) $ 0. 51 $ (viii) $ 0.501 $

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at $ P(0.5, 0) $.

(d) Sketch the curve, two of the secant lines, and the tangent line.

Chapter 2: Limits and Derivatives

Section 1: The Tangent and Velocity Problems

01:10

Calculus: Early Transcendentals

If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height in feet $ t $ seconds later is given by $ y = 40t - 16t^2 $.

(a) Find the average velocity for the time period beginning when $ t = 2 $ and lasting
(i) 0.5 seconds (ii) 0.1 seconds
(iii) 0.05 seconds (iv) 0.01 seconds
(b) Estimate the instantaneous velocity when $ t = 2 $.

Chapter 2: Limits and Derivatives

Section 1: The Tangent and Velocity Problems

01:16

Calculus: Early Transcendentals

If a rock is thrown upward on the planet Mars with a velocity of $ 10 m/s $, its height in meters $ t $ seconds after is given by $ y = 10t - 1.86t^2 $.

(a) Find the average velocity over the given time intervals:
(i) $ [1, 2] $ (ii) $ [1, 1.5] $
(iii) $ [1, 1.1] $ (iv) $ [1, 1.01] $
(v) $ [1, 1.001] $
(b) Estimate the instantaneous velocity when $ t = 1 $.

Chapter 2: Limits and Derivatives

Section 1: The Tangent and Velocity Problems

01:15

Calculus: Early Transcendentals

The table shows the position of a motorcyclist after accelerating from rest.

(a) Find the average velocity for each time period:
(i) $ [2, 4] $ (ii) $ [3, 4] $ (iii) $ [4, 5] $ (iv) $ [4, 6] $
(b) Use the graph of $ s $ as a function of $ t $ to estimate the instantaneous velocity when $ t = 3 $.

Chapter 2: Limits and Derivatives

Section 1: The Tangent and Velocity Problems

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