求极限:
limx→0∫x0(√(1+t2)-√(1-t2))/x3;
limx→0∫x0[√(1+t2)-√(1-t2)]dt/x3 =limx→0 (√(1+x2) -√(1-x2)) /3x2 =limx→0[2x/2√(1+x2)-(-2x)/2√ (1-x2)]/6x =limx→0[1/6√(1+x2)+1/6√(1-x2)] =1/3
求极限:
limx→0∫x0(√(1+t2)-√(1-t2))/x3;
limx→0∫x0[√(1+t2)-√(1-t2)]dt/x3 =limx→0 (√(1+x2) -√(1-x2)) /3x2 =limx→0[2x/2√(1+x2)-(-2x)/2√ (1-x2)]/6x =limx→0[1/6√(1+x2)+1/6√(1-x2)] =1/3