思考多项式函数f(x)=anxn 在R上,当n为奇数时
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![思考多项式函数f(x)=anxn 在R上,当n为奇数时](/uploads/image/f/4577581-37-1.jpg?t=%E6%80%9D%E8%80%83%E5%A4%9A%E9%A1%B9%E5%BC%8F%E5%87%BD%E6%95%B0f%28x%29%3Danxn+%E5%9C%A8R%E4%B8%8A%2C%E5%BD%93n%E4%B8%BA%E5%A5%87%E6%95%B0%E6%97%B6)
a1+a2+...+an=n^2*ana1+a2+...+A(n-1)=(n-1)^2*A(n-1)两式相减得an=n^2*an-(n-1)^2*A(n-1)移项得n^2*an-an=(n-1)^2*
设y=g(x)=a(x-b)(x-1)1=ab3=a(2-b)解得:a=2b=1/2g(x)=2(x-(1/2))(x-1)=2[x^2-(3/2)x+(1/2)]=2x^2-3x+1g'(x)=4x
因f'(x)=3x的平方+ax+1f(x)=X^3+AX^2/2+X+C因f(x)为奇函数,故f(0)=0,C=0f(-x)=-X^3+AX^2/2-X=-X^3-AX^2/2-XA=0,f'(x)=
f(1)=n^2,a1+a2+…+an=n^2,即Sn=n^2,所以a1=S1=1,n≥2时,an=Sn-S(n-1)=n^2-(n-1)^2=2n-1.∴an=2n-1,n∈N+.
由题意有f(1)=a1+a2+…+an=(a1+an)*n/2=n^2从而a1+an=2n2a1+(n-1)d=2n…①f(-1)=-1a1+a2-a3+…+(-1)^n*an若n为奇数f(-1)=-
fn(1)=a1+a2+...+an=na1+n(n-1)/2=4n+d*n(n-1)/2所以4n+d*n(n-1)/2=(3n^2+bn)/2,也就是8+d(n-1)=3n+b可见d=3,b=5an
f(1)=a1+a2+……+an=(a1+an)*n/2=n^2=>a1+an=2n=>2a1+(n-1)d=2n……1f(-1)=-1a1+a2-a3+……+(-1)^n*an若n为奇数f(-1)=
(1)f(1)=n^2,n=1时,a1=1^2=1,又f(1)=n^2=(a1+an)*n/2=n^2得an=2n-a1=2n-1(2)f(0.5)=0.5*a1+0.5^2*a2+.+0.5^n*a
反证法.设存在实数x0使f[f(x0)]=g[g(x0)],则g{f[f(x0)]}=g{g[g(x0)]},由已知,上式左端=f{g[f(x0)]}=f{f[g(x0)]},令y0=g(x0),则f
f(x)=∫f'(x)dx=x³/3+2x²+cf(-3)=-9+18+c=10c=1f(x)=x³/3+2x²+1
函数f(x)是二次多项式.设y=f(x)=kx²+mx+c,则f'(x)=2kx+m,f"(x)=2k当点x=a时,有f‘(a)=2ka+m,f"(a)=2k.所以,k=f"(a)/2及f'
f(x+1)+f(x-1)=2x^2-4xf(x)比为二次函数设f(x)=ax^2+bx+cf(x+1)+f(x-1)=a(x+1)^2+b(x+1)+c+a(x-1)^2+b(x-1)+c=2ax^
1)f(1)=a1+a2+...+an=n^2a1+a2+...an-1=(n-1)^2两式相减得an=n^2-(n-1)^2=2n-12)f(x)=x+3x^2+.(2n-1)x^nf(1/3)=1
反证法.假设f(x)=sinx是n次多项式.则f(x)的n阶导数等于n!,f(x)的n+1阶导数恒等于0.而sinx的n+1阶导数为sin[x+(n+1)π/2],这不是常值函数,产生矛盾,故假设错误
f(1)=a1+a2+...+an=n^2Sn=n(a1+an)/2=n^2=>(a1+an)/2=[a1+a1+(n-1)d]/2=n...1式f(-1)=-a1+a2-a3+...+an=(a2-
设f(x)=ax^2+bx+c则f(x+1)+f(x-1)=a(x+1)^2+b(x+1)+c+a(x-1)^2+b(x-1)+c=2ax^2+2bx+2a+2c所以2a=2,2b=-2,2a+2c=
f(1)=a1+a2+a3+.+an=n^2=Sa=S-S=n^2-(n-1)^2=2n-1a=S=1所以a=2n-1
要使函数f(x)=lg(x2-anx+bn)定义域为R,则必须满足△=a2n−4bn<0,成立.①a0←1,b0←-1,n←1,n<5,运行循环结构,输出a1←1+1,b1←-1+2,不满足△<0;②
f'(x)是2次多项式,即是二次函数且与x轴交点为(0,0),(2,0)设f'(x)=kx(x-2)再将点(1,-3)代入,得:k=3∴f'(x)=3x(x-2)=3x^2-6xf(x)是三次多项式函