CRL 5.4 MrG Tangents and Normals 2012.0119

3609 days ago by calcpage123

#1) var('a') a=1 f(x)=sqrt(x^3/(2*a-x)) h(x)=diff(f(x),x) m=h(a) t(x)=m*(x-a)+a n(x)=-1/m*(x-a)+a plot([f(x),t(x),n(x)],xmin=0,xmax=1.5,aspect_ratio=1) 
       
#7) a=5 f(x)=(a/2)*(e^(x/a)+e^(-x/a)) h(x)=diff(f(x),x) m=h(a/2) t(x)=m*(x-a/2)+f(a/2) n(x)=-1/m*(x-a/2)+f(a/2) plot([f(x),t(x),n(x)],xmin=-a,xmax=a,aspect_ratio=1) 
       
#8) a=-.75 f(x)=x^3 h(x)=diff(f(x),x) t(x)=h(a)*(x-a)+f(a) n(x)=-1/h(a)*(x-a)+f(a) plot([f(x),t(x),n(x)],aspect_ratio=1) 
       
f(x)=(log(1-x)-sin(x)) g(x)=(1-cos(x)^2) h(x)=f(x)/g(x) show(f(x)) show(g(x)) show(h(x)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\log\left(-x + 1\right) - \sin\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\cos\left(x\right)^{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{\log\left(-x + 1\right) - \sin\left(x\right)}{\cos\left(x\right)^{2} - 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\log\left(-x + 1\right) - \sin\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\cos\left(x\right)^{2} + 1
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{\log\left(-x + 1\right) - \sin\left(x\right)}{\cos\left(x\right)^{2} - 1}
show(f(0)) show(g(0)) show(diff(f(x),x)) show(diff(g(x),x)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{x - 1} - \cos\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(x\right) \cos\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{x - 1} - \cos\left(x\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sin\left(x\right) \cos\left(x\right)