3x2+x+1x<0 例26设f(x)={k SInx +1y>0 √x 当k为何值时,f(x)在x=0点连续 解∵f(0)=k,且limf(x)=lim(3x2+x+1)=1 x→0 x→0 sIns limf(x)=lm(产+1)=1 lim f(x)=lim f(x=1 故当∫(0)=k=1时,∫(x)在x=0处连续9 例26.设 2 3 1 0 ( ) 0 sin 1 0 x x x f x k x x x x  + +     = =    +   当 k 为何值时, ƒ(x)在 x = 0点连续. 解 2 0 0 (0) , lim ( ) lim(3 1) 1 x x f k f x x x → → − − = = + + = 且 故 当 f k f x x (0) 1 , ( ) 0 . = = = 时 在 处连续 0 0 sin lim ( ) lim( 1) 1 x x x f x x → → + + = + = 0 0 lim ( ) lim ( ) 1 x x f x f x  = = → → − +