The-Organic-Chemistry-Tutor
The video covers a variety of introductory physics concepts. It begins by differentiating between distance and displacement, and then explains scalar and vector quantities. The video then explores speed, velocity, and acceleration, how they are defined, and how they relate to each other. Additionally, projectile motion is explained through examples, and the concept of friction is introduced. Finally, the video covers Newton's laws of motion and demonstrates how they apply to a practical problem involving an object's acceleration. The video is ideal for individuals who wish to have an elementary understanding of basic physics concepts.
The video covers various techniques to evaluate limits, including direct substitution, factoring, and using the common denominator and conjugate methods for complex fractions and radicals. The concept of one-sided limits is introduced, along with vertical asymptotes and jump discontinuities. The distinction between removable and non-removable discontinuities is also explained. The instructor provides multiple examples and demonstrates the graphical method of finding the limit.
This video explains how to perform elementary row operations using matrices for solving equations. The examples given include multiplying all elements in a row by a scalar, swapping rows, and adding two rows together by scaling one and adding it to the other. The video also shows how to perform a row operation with no attachment to any particular row, and how to rewrite the matrix after the row operation is performed. By following these methods, simple changes can be made to rows within matrices to help solve equations using the elementary row operation method.
The video discusses the comparison between two investments, one with a 7.3% interest rate compounded quarterly and the other with a 7.4% interest rate compounded annually, over a span of 10 years. The investment with compounding quarterly provides interest four times a year, resulting in greater returns due to the power of compounding, as compared to once a year with the annually compounded investment. The video also examines other factors that can increase the investment's rate of return, such as an increase in the interest rate, the frequency of interest payments, and the length of time the investment has been working.
This video section teaches how to find the X and Y components of a vector given its magnitude and direction by using trigonometry. The instructor explains that the X component is found by multiplying the force by the cosine of the angle, and the Y component is found by multiplying the force by the sine of the angle. This comes from the SOHCAHTOA rule in trigonometry, where sine is opposite over hypotenuse and cosine is adjacent over hypotenuse. The instructor provides examples and demonstrates how to use these equations to find the components of a force vector.
This video teaches how to find derivatives using inverse hyperbolic functions using various formulas such as the derivative of inverse hyperbolic sine, cosine, tangent, cosecant, and cotangent functions. The video provides several examples to demonstrate how to apply the power rule and chain rule to find the derivative, including finding the derivative of an expression involving a product rule problem with six times the inverse hyperbolic sine of 3x and minus two square root one plus 9x squared. The YouTuber applies the power rule and the derivative 18x to get negative 18x over the square root of one plus 9x squared and simplifies the expression to get six inverse hyperbolic sine of 3x, allowing viewers to derive the derivative of inverse hyperbolic functions.
The video discusses how to evaluate the limits of hyperbolic functions by drawing their graphs, as it helps to determine the Y values as X approaches either infinity or zero from either side. The video provides examples for various hyperbolic functions, and mentions that using graphing can be an effective method to solve hyperbolic function limit problems. They also evaluated the hyperbolic cotangent and found that it has two horizontal asymptotes and a vertical asymptote; the limits were evaluated for x approaching negative infinity, positive infinity, and zero by analyzing the graph. It was concluded that understanding the graphs of hyperbolic functions can be helpful in evaluating their limits.
This video covers the graphs of inverse hyperbolic functions, including hyperbolic tangent, cotangent, cosecant, and secant. The graphs are obtained by reflecting the original graphs across the line y=x. The domains and ranges of the regular and inverse functions are related, with the domain becoming the range and vice versa. The speaker provides examples and explains the asymptotes and restrictions for each inverse function, as well as their usefulness in solving problems. The importance of comparing regular and inverse graphs to understand their properties and relationships is emphasized.
This video covers the topic of evaluating inverse hyperbolic functions and provides formulas and examples on how to do so. The speaker emphasizes the importance of switching X and Y when dealing with inverse functions and gives formulas for various inverse hyperbolic functions such as cosine, sine, tangent, cotangent, secant, and cosecant. Additionally, the domains for each of these functions are discussed, including potential undefined fractions or values. Finally, the speaker confirms the answers using the exponential function of hyperbolic sine.
The video covers the topic of finding derivatives of hyperbolic functions using various rules such as the chain rule and the product rule. The derivatives of hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and cotangent are explained using the derivative rules. The speaker also demonstrates examples of finding the derivatives of hyperbolic functions and natural logarithms of hyperbolic functions. The video highlights the similarities between the rules used in finding derivatives of hyperbolic functions and those used for other functions.
