Question

HELP: CONTINUITY B=?
(attached below)

Answer 1

plug in x = 3. You'll get a number for the first function and set the second function equal to that value. Plug in 3 for x and solve for b.

Answer 2

in the second function

Answer 3

i did i got it wrong.. :/

Answer 4

can you show me how you would do it?

Answer 5

@pgpilot326

Answer 6

From the first equation:\[4(3)-6=12-6=6\]
Thus -7(x)+b = 6 when x=3. So
\[-7(3)+b=6 \rightarrow -12+b=6 \rightarrow b=21+6=27\]
Is this what you got?

Answer 7

yes, i missed one step, thank you.

Answer 8

I got it, thanks alot.

Answer 9

Please note a function is continuos at x=a, if (1) L.H.L=R.H.L
(2) \[\lim_{x \rightarrow a} f(x)=f(a)\]
\[\lim_{x \rightarrow 3-}f \left( x \right)=\lim_{x \rightarrow3-}\left( 4x-6 \right)\]
\[put x=3-h,h>0,h \rightarrow 0 as x \rightarrow 3-\]
\[\lim_{x \rightarrow 3-}f \left( x \right)=\lim_{h \rightarrow 0}\left\{ 4\left( 3-h \right)-6 \right\}=4\left( 3-0 \right)-6=6 \]
\[\lim_{x \rightarrow 3+}f \left( x \right)=\lim_{x \rightarrow 3+} \left( -7x+b \right)\]
\[put x=3+h,h \rightarrow 0,as x \rightarrow 3+\]
\[\lim_{x \rightarrow 3+} f \left( x \right)=\lim_{h \rightarrow 0} \left\{- 7\left( 3+h \right)+b \right\}\]=-7(3+0)+b=-21+b
Because f(x) is continuous at all real values
\[Hence \lim_{x \rightarrow3-}f(x)=\lim_{x \rightarrow 3+} f(x)\]
6=-21+b
b=6+21=27