2024/G1/2: Difference between revisions
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==2.7 DERIVATIVES AND RATES OF CHANGE == | ==2.7 DERIVATIVES AND RATES OF CHANGE == | ||
To find the Tangent Line we use <math> \lim_{h \to | To find the Tangent Line we use <math> \lim_{h \to 0}\frac{f(x+h)-f(x)}{h} | ||
</math><br> 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}\frac{\cancel{h} | |||
</math><br> | </math><br> | ||
Revision as of 21:07, 30 March 2023
2.2 THE LIMIT OF A FUNCTION
Notes go here for 2.2... example:
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 \lim_{z\to z_0} f(z)=f(z_0)}
2.3 CALCULATING LIMITS USING THE LIMIT LAWS
2.5 CONTINUITY
2.6 LIMITS AT INFINITY; HORIZONTAL ASYMPTOTES
2.7 DERIVATIVES AND RATES OF CHANGE
To find the Tangent Line we use 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 \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}\frac{\cancel{h}
</math>
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)} }
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 }