几道高数题目:1、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+21、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+23、做函数的图形 y=[(x-1)/(x-2)
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![几道高数题目:1、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+21、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+23、做函数的图形 y=[(x-1)/(x-2)](/uploads/image/z/2686985-17-5.jpg?t=%E5%87%A0%E9%81%93%E9%AB%98%E6%95%B0%E9%A2%98%E7%9B%AE%3A1%E3%80%81%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dcosx%2F%281%2Bsinx%29%2C%E6%B1%82f%E2%80%99%28%CF%80%2F4%29+2%E3%80%81%E6%B1%82%E6%9E%81%E9%99%90Limx%E2%86%92%E2%88%9E%5B+%28X%2B1%29%2F%EF%BC%88X-1%EF%BC%89%5D+%5Ex%2B21%E3%80%81%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dcosx%2F%281%2Bsinx%29%2C%E6%B1%82f%E2%80%99%28%CF%80%2F4%29+2%E3%80%81%E6%B1%82%E6%9E%81%E9%99%90Limx%E2%86%92%E2%88%9E%5B+%28X%2B1%29%2F%EF%BC%88X-1%EF%BC%89%5D+%5Ex%2B23%E3%80%81%E5%81%9A%E5%87%BD%E6%95%B0%E7%9A%84%E5%9B%BE%E5%BD%A2+y%3D%5B%EF%BC%88x-1%EF%BC%89%2F%EF%BC%88x-2%EF%BC%89%26%23)
几道高数题目:1、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+21、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+23、做函数的图形 y=[(x-1)/(x-2)
几道高数题目:1、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+2
1、设函数f(x)=cosx/(1+sinx),求f’(π/4)
2、求极限Limx→∞[ (X+1)/(X-1)] ^x+2
3、做函数的图形 y=[(x-1)/(x-2)²]-1
几道高数题目:1、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+21、设函数f(x)=cosx/(1+sinx),求f’(π/4) 2、求极限Limx→∞[ (X+1)/(X-1)] ^x+23、做函数的图形 y=[(x-1)/(x-2)
很可惜,楼上第二题,解错了.
∵f'(x)=[-sin(x)-sin^2(x)-cos^2(x)]/(1+sinx)^2=[-sin(x)-1]/(1+sinx)^2=-1/(1+sinx) ∴f'(π/4)=-1/(1+√2/2)=-2/(2+√2)=-2+√2 Lim[x→∞][ (X+1)/(X-1)] ^x+2 =Limx→∞[...
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∵f'(x)=[-sin(x)-sin^2(x)-cos^2(x)]/(1+sinx)^2=[-sin(x)-1]/(1+sinx)^2=-1/(1+sinx) ∴f'(π/4)=-1/(1+√2/2)=-2/(2+√2)=-2+√2 Lim[x→∞][ (X+1)/(X-1)] ^x+2 =Limx→∞[ (1+1/x)^x/(1-1/x)^x+2 =e^2+2 定义域:x≠2 y'=[(x-2)^2-2(x-1)(x-2)]/(x-2)^4=[x-2-2x+2]/(x-2)^3=-x/(x-2)^3 y''=-1/(x-2)^3+3x/(x-2)^4=(2x+2)/(x-2)^4 (-∞,-1) -1 (-1,0 ) 0 (0,2) (2,+∞) f‘(x) - - - + - f''(x) - + + + f(x) 减凸 拐点 减凹 极小-5/4 增凹 减凹 渐近线 y=-1 x=2 如下图:
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