Answer
$0$
Work Step by Step
$\lim _{x\rightarrow -b}\dfrac {\left( x+b\right) ^{7}+\left( x+b\right) ^{10}}{4\left( x+b\right) }=\dfrac {\left( x+b\right) ^{7}\left( 1+\left( x+b\right) ^{3}\right) }{4\left( x+b\right) }=\dfrac {\left( x+b\right) ^{6}\left( 1+\left( x+b\right) ^{3}\right) }{4}=\dfrac {0\times \left( 1+0\right) }{4}=0$
