当α,β取何值时,函数f(x)={(x^α cos〖1/x〗 ,x>0;β+sin〖x^2 〗 ,x≤0)┤在x=0处连续:何时在x=0处可导
问题描述：
当α,β取何值时,函数f(x)={(x^α cos〖1/x〗 ,x>0;β+sin〖x^2 〗 ,x≤0)┤在x=0处连续:何时在x=0处可导
答
f(x) = x^α cos (1/x) ; x >0= β+sin(x^2) ; x≤0f(0+) = lim(x->0+){ x^α cos (1/x) }=0f(0-) =lim(x->0-){ β+sin(x^2) }= βf is cts on x = 0 ,=> β =0f(x) = x^α cos (1/x) ; x >0= sin(x^2) ; x≤0x >0f'...