What value must be chosen for a to make tis function continuous at -1? 2x^3+x^2+7x+8/x+1 when x

Question

What value must be chosen for a to make tis function continuous at -1? 2x^3+x^2+7x+8/x+1 when x<-1 and by -x^2+2x+a when -1< or = x

nenadmatematika · Answer

lim of the function when x comes to -1 from the left side must be equal to the lim of the function when x comes to -1 from the right side. Make that equality and you'll get value for a...be careful at that first function, you'll get 0/0 if you plug in x=-1immediately, so, to avoid that, use a little bit of algebra knowledge and you'll get value for lim

anonymous · Answer

can you give me a step by step way to solve it please?

nenadmatematika · Answer

ok wait a minute

nenadmatematika · Answer

you can write down the first function like this:$$(x+1)(2x^2-x+8)/(x+1)=2x^2-x+8$$
now if you plug in x=-1 you'll get: $$2*1+1+8=11$$
that's the limit as x approaches -1 from the left side...now if you plug in x=-1 into the other function you'll get -3+a....so you must say 11=-3+a and a=14

anonymous · Answer

perfect thank you!

nenadmatematika · Answer

you're welcome :D