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1-6.txt
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1-6.txt
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kill(all)$
print("Раздел 1")$
print("5.7")$
lim57:'limit(((sum(2*i-1,i,1,n))/(n+3))-n, n, inf)$
print(lim57,"=", ev(lim57,nouns))$
kill(all)$
print("7.7")$
lim77:'limit((9*x^2-1)/(x+1/3),x,-1/3)$
print(lim77,"=", ev(lim77,nouns),"=",-6)$
kill(all)$
print("12.7")$
lim127:'limit((sin(x)^2-tan(x)^2)/(x-%pi)^4,x,%pi)$
print(lim127,"=", ev(lim127,nouns))$
kill(all)$
print("19.7")$
f(x):=(2-x/3)^(sin(pi)*x)$
lim197:'limit(f(x),x,3)$
print(lim197,"=", ev(lim197,nouns))$
kill(all)$
print("Раздел 2")$
print("2.7")$
x0:4$
f(x) := (1+sqrt(x))/(1-sqrt(x))$
k:1/diff(f(x),x,1)$
kev:ev(k,x=4)$
y(x) := f(x0) - kev*(x-x0)$
print("y(x) = ", y(x))$
kill(all)$
print("3.7")$
func:f(x) := atan(sinh(x)) + sinh(x)*log(cosh(x));
print("dy = ", diff(f(x),x))$
kill(all)$
print(11.7)$
func:f(x):=(cot(3*x))^(2*exp(x));
dy:diff(f(x),x,1)$
print("dy =",dy)$
kill(all)$
print("15.7")$
x(t):=cat(exp(t)*2)$
y(t):=log(tan(exp(t)))$
print("x(t) =", x(t))$
print("y(t) =", y(t))$
a:diff(y(t),t,1)$
b:diff(x(t),t,1)$
a(t):=a/b$
print("a(t) =", a(t))$
kill(all)$
print("17.4")$
y(x):= x/(2*(3*x+2))$
a:diff(y(x),x,3)$
print("y(x) =",y(x))$
print("y(x)''' =",a)$
kill(all)$
print("Раздел 3")$
print("6.7")$
y(x):=(2*x^2-6)/(x-2)$
print("y(x) =",y(x))$
wxplot2d(y(x), [x,-5,5], [y,-5,5])$
kill(all)$
print("Раздел 4")$
print("4.7")$
func:f(x):=(8*x-atan(2*x))/(1+4*x^2);
f:'integrate(f(x),x,0,1/2)$
a:integrate(f(x),x,0,1/2)$
print(f ,"=",a)$
kill(all)$
print("8.4")$
From:2*atan(1/3)$
To:2*atan(1/2)$
f(x):=(1/(sin(x)*(1-sin(x))))$
f:'integrate(f(x),x,From,To)$
a:integrate(f(x),x,From,To)$
print(f ,"=",a)$
kill(all)$
print("14.7")$
From:0$
To:%pi/2$
f(x):=(cos(x)*sin(x)^2)$
f:'integrate(f(x),x,From,To)$
a:integrate(f(x),x,From,To)$
print(f ,"=",a)$
kill(all)$
print("17.7")$
From:1/4$
To:1$
func:f(x):=(2+asin(sqrt(x))+sqrt(x-x^2));
df(x):=diff(f(x),x)$
L(x):=sqrt(1+(df(x))^2)$
f:'integrate(L(x),x,From,To)$
a:integrate(L(x),x,From,To)$
print(f ,"=",a)$
kill(all)$
print("Раздел 5")$
print("4.7")$
differ:'diff(y,x)-y/x=x*sin(x);
intergral:ode2(differ,y,x);
x0:%pi/2$
y0:1$
answer:ic1(intergral, x=x0, y=y0);
kill(all)$
print("14.7")$
differ:'diff(y,x,2)+2*'diff(y,x)=e^x*(sin(x)+cos(x));
answer:ode2(differ,y,x);
kill(all)$
load("simplify_sum")$
print("Раздел 6")$
print("1.7")$
func:f(n):=8/(n^2-8*n+15)$
sum17:sum(f(n),n,6,inf)$
sum17ex:simplify_sum(sum17)$
print(sum17,"=", sum17ex)$
kill(all)$
load("simplify_sum")$
print("4.7")$
func:f(n):=(1/n!)*atan(5/n)$
sum:sum(f(n),n,1,inf);
print("По Даламберу")$
a:f(n)$
b:f(n+1)$
ans:'limit(b/a,n,inf)$
print(ans,"=", ev(ans, nouns))$
print("Ряд сходится, так как предел равен 0")$
kill(all)$
load("simplify_sum")$
print("5.7")$
func:f(n):=((4*n-3)/(5*n+1))**n^2$
sum57:sum(f(n),n,1,inf);
lim57:'limit(f(n)^1/n, n, inf)$
lim57ex:'limit(f(n)^1/n, n, inf)$
print(lim57,"=", ev(lim57ex,nouns))$
print("Так как предел меньше 1, то ряд сходится", c)$