_ x ( x+6 x+1 )^ x+4 is equal to

Step-by-step solution

aligned & _ x ( x+6 x+1 )^ x+4 & _ x ( 1+ 6 x 1+ 1 x )^ x+4 & x , 1+ 6 x 1,1+ 1 x 1 & 1+ 6 x 1+ 1 x 1 & and x+4 aligned It is an indeterminate form of 1^ . Now, _ x ( x+6 x+1 )^ x+4 =e^ _ x - ( x+6 x+1 -1 ) x+4 aligned & =e^ _ x - ( x+6-x-1 x+1 ) x+4 & =e^ _ x - 5(x+4) x+1 =e^ _ x - x (1+ 4 x ) x (1+ 1 x ) & =e^ 5 (1+0) (1+0) & [ x , 1 x 0 ] & =e^5 & aligned