2024/G1/2

2.2 THE LIMIT OF A FUNCTION

Notes go here for 2.2... example:
$\lim _{z\to z_{0}}f(z)=f(z_{0})$

2.7 DERIVATIVES AND RATES OF CHANGE

To find the Tangent Line we use $\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}$
We later apply the points on which we want to find the slope. Ex:</math>f(x)=x^2 f'(x)=\lim{h \to 0}\frac{f(x+h)-f(x)}{h}= \lim{h \to 0}\frac{(x+h)^2-x^2}{h}= \lim{h \to 0}\frac{x^2+2xh+h^2-x^2)}{h}=\lim{h \to 0}\frac{h^2+2xh}{h}=\lim{h \to 0} </math>

2.8 THE DERIVATIVE AS A FUNCTION

${\frac {d}{dx}}[c]=0$
${\frac {d}{dx}}[c\cdot f(x)]=c\cdot {\frac {d}{dx}}[f(x)]$

${\frac {d}{dx}}[f(x)\pm g(x)]={\frac {d}{dx}}[f(x)]\pm {\frac {d}{dx}}[g(x)]$
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [x^n] = n \cdot x^{(n-1)} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [a^x] = \ln(a)a^x }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [e^x] = e^x }