Kalkulus I.
J\303\241rai Antal
Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
3. Hat\303\241r\303\251rt\303\251k
restart;
3.1. Hat\303\241r\303\251rt\303\251k \303\251s folytonoss\303\241g
3.1.2. Bels\305\221, izol\303\241lt \303\251s torl\303\263d\303\241si pontok.
3.1.21. Jobb \303\251s bal oldali folytonoss\303\241g.
3.1.30. P\303\251ld\303\241k.
limit(signum(x),x=0,right); limit(signum(x),x=0,left);
limit(signum(x),x=0); limit(signum(x),x=0,complex);
limit(abs(signum(x)),x=0); limit(abs(signum(x)),x=0,complex);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
3.1.33. P\303\251lda.
limit(1/x,x=0); limit(1/x,x=0,complex);
limit(1/x,x=0,right); limit(1/x,x=0,left);
limit(1/x,x=infinity); limit(1/x,x=-infinity);
limit(1/x,x=infinity,complex);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
3.3. Hatv\303\241nysorok.
restart;
3.3.10. Motiv\303\241ci\303\263.
3.3.11. Trigonometrikus \303\251s hiperbolikus f\303\274ggv\303\251nyek.
(exp(I*z)+exp(-I*z))/2; convert(%,trig);
(exp(I*z)-exp(-I*z))/(2*I); convert(%,trig);
sum((-1)^n*z^(2*n)/(2*n)!,n=0..infinity);
sum((-1)^n*z^(2*n+1)/(2*n+1)!,n=0..infinity);
exp(I*t); convert(%,trig);
cos(z)^2+sin(z)^2; simplify(%);
cos(z1+z2); expand(%); sin(z1+z2); expand(%);
(exp(z)+exp(-z))/2; convert(%,trigh);
(exp(z)-exp(-z))/2; convert(%,trigh);
sum(z^(2*n)/(2*n)!,n=0..infinity);
sum(z^(2*n+1)/(2*n+1)!,n=0..infinity);
cosh(z)^2-sinh(z)^2; simplify(%);
cosh(z1+z2); expand(%); sinh(z1+z2); expand(%);
plots[complexplot3d](exp(z),z=-2-2*Pi*I..2+2*Pi*I);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn