>> int(x^4/(917+4*x^2),x) ans =
(917*917^(1/2)*atan((2*917^(1/2)*x)/917))/32 - (917*x)/16 + x^3/12 (5)
>> taylor(sqrt(917/1000+x),9,0) ans = -
(13092041015625000000*917^(1/2)*1000^(1/2)*x^8)/499982363688330647123041
+
(16113281250000000*917^(1/2)*1000^(1/2)*x^7)/545237037828059593373
-
(2929687500000*917^(1/2)*1000^(1/2)*x^6)/84941118215930767 + (3906250000*917^(1/2)*1000^(1/2)*x^5)/92629354652051 - (39062500*917^(1/2)*1000^(1/2)*x^4)/707094310321 (62500*917^(1/2)*1000^(1/2)*x^3)/771095213 (125*917^(1/2)*1000^(1/2)*x^2)/840889
+ - +
(917^(1/2)*1000^(1/2)*x)/1834 + (917^(1/2)*1000^(1/2))/1000
(6)
>> vpa(subs(diff(exp(sin(1/x)),x,3),917),17) ans =
-0.0000000000085039379376257672 4.(1)
>> A=[-2,1,1;0,2,0;-4,1,9.17];inv(A) ans =
-0.6395 0.2849 0.0697 0 0.5000 0 -0.2789 0.0697 0.1395
>> A=[-2,1,1;0,2,0;-4,1,9.17];eig(A) ans =
-1.6296 8.7996 2.0000
>> [P,D]=eig(A) P =
-0.9377 -0.0922 0.2425 0 0 0.9701 -0.3473 -0.9957 -0.0000 D =
-1.6296 0 0 0 8.7996 0 0 0 2.0000 P的列向量为特征向量。
(2) 求点(1,1,4)到直线L: x?3?y?z?1?102
>> M0=[1,1,4];M1=[3,0,1];M0M1=M1-M0; v=[-1,0,2];
d=norm(cross(M0M1,v))/norm(v)
的距离
d =
1.0954
5、已知f(x)?图）
(1)??1时,?＝0，－，11，在同一坐标系里作图
12??e?(x??)22?2（要求贴,分别在下列条件下画出f(x)的图形：
>> syms x;
>> fplot('(1/sqrt(2*pi))*exp(-((x)^2)/2)',[-3,3],'r') >> hold on
>> fplot('(1/sqrt(2*pi))*exp(-((x-1)^2)/2)',[-3,3],'y') >> hold on
>> fplot('(1/sqrt(2*pi))*exp(-((x+1)^2)/2)',[-3,3],'g') >> hold off
(2)?＝0时,?＝1，，24，在同一坐标系里作图。
>> syms x;
fplot('(1/sqrt(2*pi))*exp(-((x)^2)/2)',[-3,3],'r'); hold on;
fplot('(1/(sqrt(2*pi)*2))*exp(-((x)^2)/(2*2^2))',[-3,3],'y'); hold on;
fplot('(1/(sqrt(2*pi)*4))*exp(-((x)^2)/(2*4^2))',[-3,3],'g'); hold off
6、画下列函数的图形：（要求贴图）
??x?usint?（1）?y?ucost?t?z?4?0?t?20 0?u?2
>> ezmesh('u*sin(t)','u*cos(t)','t/4',[0,20,0,2])