2024/G1/2

2.2 THE LIMIT OF A FUNCTION

Notes go here for 2.2... example:
$\lim _{z\to z}[f(x)g(x])=c\cdot [\lim _{x\to a}f(x)]$

2.3 CALCULATING LIMITS USING THE LIMIT LAWS

$\lim _{x\to a}=c\cdot [\lim _{x\to a}f(x)]$

2.6 LIMITS AT INFINITY; HORIZONTAL ASYMPTOTES

Horizontal Asymptote or H.A Failed to parse (unknown function "\math"): {\displaystyle \lim_{x \to \infty} <\math><br> ==2.7 DERIVATIVES AND RATES OF CHANGE == To find the Tangent Line we use <math> \lim_{h \to 0}\frac{f(x+h)-f(x)}{h} }
We later apply the points on which we want to find the slope. $f(x)=x^{2}f'(x)=\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}=\lim _{h\to 0}{\frac {(x+h)^{2}-x^{2}}{h}}=\lim _{h\to 0}{\frac {x^{2}+2xh+h^{2}-x^{2})}{h}}=\lim _{h\to 0}{\frac {h^{2}+2xh}{h}}=\lim _{h\to 0}{\frac {({\cancel {h}})(h+2x)}{\cancel {h}}}$
$=\lim _{h\to 0}h+2x=(0)+2x$

2.8 THE DERIVATIVE AS A FUNCTION

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