document.write( "Question 1017899: Find the values of a and b that will make the function continuous every where. Justify.\r
\n" ); document.write( "\n" ); document.write( "f(x)=
\n" ); document.write( "x^2+11x+10/x+1, x<-1
\n" ); document.write( "e^2ax , -1<= x <= 1
\n" ); document.write( "bx^2-ax, x>1\r
\n" ); document.write( "\n" ); document.write( "thank you in advance! \n" ); document.write( "

Algebra.Com's Answer #634173 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
I believe what you meant is
\n" ); document.write( " $\"f%28x%29\"$ $\"%22=%22\"$

\n" ); document.write( "
\n" ); document.write( "The pieces of that function are continuous in
\n" ); document.write( " $\"%22%28%22\"$ $\"-infinity\"$ $\"%22%2C%22\"$ $\"%22-+1+%29%22\"$ , $\"%22%5B%22\"$ $\"-1\"$ $\"%22%2C%22\"$ $\"%221+%29%22\"$ , and $\"%22%28+1%22\"$ $\"%22%2C%22\"$ $\"infinity\"$ $\"%22%29%22\"$ .
\n" ); document.write( "We just have to make it continuous at $\"x=-1\"$ and $\"x=1\"$ .
\n" ); document.write( "
\n" ); document.write( "For $\"x=-1\"$ , we have $\"f%28-1%29=e%5E%28-2a%29\"$ .
\n" ); document.write( "For $\"x%3C-1\"$ , $\"f%28x%29=%28x%5E2%2B11x%2B10%29%2F%28x%2B1%29=%28x%2B1%29%28x%2B10%29%2F%28x%2B1%29=x%2B10\"$ , and
\n" ); document.write( " $\"lim%28x-%3E-1%2Cf%28x%29%29=lim%28x-%3E-1%2Cx%2B10%29=-1%2B10=9\"$ ,
\n" ); document.write( "so for $\"f%28x%29\"$ to be continuous at $\"x=-1\"$ ,
\n" ); document.write( "it must be $\"e%5E%28-2a%29=9\"$ --> $\"e%5E%28-2a%29=3%5E2\"$ --> $\"-2a=2ln%283%29\"$ --> $\"highlight%28a=-ln%283%29%29\"$
\n" ); document.write( "
\n" ); document.write( "For $\"x=1\"$ , we have $\"f%281%29=e%5E%282a%29\"$ .
\n" ); document.write( "For $\"x%3E1\"$ , $\"f%28x%29=bx%5E2-ax\"$ , and
\n" ); document.write( " $\"lim%28x-%3E1%2Cf%28x%29%29=lim%28x-%3E1%2Cbx%5E2-ax%29=b-a\"$ ,
\n" ); document.write( "so for $\"f%28x%29\"$ to be continuous at $\"x=-1\"$ ,
\n" ); document.write( "it must be $\"b-a=e%5E%282a%29\"$ .
\n" ); document.write( "Since we knew that
\n" ); document.write( " $\"system%28e%5E%28-2a%29=9%2C%22and%22%2Ca=-ln%283%29%29\"$ --> $\"system%28e%5E%282a%29=1%2F9%2C%22and%22%2Ca=-ln%283%29%29\"$ ,
\n" ); document.write( "substituting into $\"b-a=e%5E%282a%29\"$ , we get $\"b%2Bln%283%29=1%2F9\"$ --> $\"highlight%28b=ln%283%29%2B1%2F9%29\"$ \n" ); document.write( "

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