Derivative of sin x by First Principles

Derivative of sin x by First Principles

Method 1 Required Trigonometric Formula \( \displaystyle \sin A-\sin B = 2 \cos \left( \frac{A+B}{2} \right) \sin \left( \frac{A-B}{2} \right) \) \( \require{ASMsymbols} \displaystyle \begin{align} \frac{d}{dx} \sin x &= \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h} \\ &= \lim_{h \to 0} \frac{2 \cos \left(x+\frac{h}{2} \right) \sin \frac{h}{2}}{h} &\color{green}{\text{by the given formula above}} \\ &= \lim_{u \to […]

How to Find the Centre, Period, Velocity, Acceleration and Times of Simple Harmonic Motion Explained

How to Find the Centre, Period, Velocity, Acceleration and Times of Simple Harmonic Motion Explained

Simple Harmonic Motion is a specific type of periodic motion where is any motion whose displacement-time equation, apart from the constants, is a single sine and/or cosine function. Of particular importance is a certain kind of rectilinear motion known as Simple Harmonic Motion. A particle is said to be undergoing in simple harmonic motion with […]

Read This Simple Work for Definite Integrals by U-SUBSTITUTION Method Explained in 3 Distinct Examples and Video Lessons

Read This Simple Work for Definite Integrals by U-SUBSTITUTION Method Explained in 3 Distinct Examples and Video Lessons

U-substitution in definite integrals is very similar to the method in indefinite integrals, while the initial bounds (usually x-values) need to be changed to the corresponding u-values for upper and lower limits. You need to account for the limits of the integration. Alternatively, you can integrate the integral expressions using u-substitutions, then change u-expressions back […]