To determine

To evaluate:  limx→0cosx−1+12x2x4

Answer

limx→0cosx−1+12x2x4= 124

Explanation

limx→0cosx−1+12x2x4 (00Form)Applying l'Hospital's rule, we get=limx→0−sinx+x4x3 (00Form)Applying l'Hospital's rule again, we get=limx→0−cosx+112x2 (00Form)Applying l'Hospital's rule again, we get=limx→0sinx24x=124limx→0sinxx=124(1)=124

Conclusion: The value of the limit is limx→0cosx−1+12x2x4= 124