Question

Find the values of ( a ) and ( b ) that make ( f ) continuous everywhere. [ f(x)=left{egin{array}{ll} frac{x^{2}-4}{x-2} & ext { if } x<2 \ a x^{2}-b x+3 & ext { if } 2 leq x<3 \ 2 x-a+b & ext { if } x geq 3 end{array} ight. ]

          Find the values of ( a ) and ( b ) that make ( f ) continuous everywhere.
[
f(x)=left{egin{array}{ll}
frac{x^{2}-4}{x-2} & 	ext { if } x<2 \
a x^{2}-b x+3 & 	ext { if } 2 leq x<3 \
2 x-a+b & 	ext { if } x geq 3
end{array}
ight.
]

$Find the values of ( a ) and ( b ) that make ( f ) continuous everywhere. [ f(x)=lefteginarrayll fracx^2-4x-2 ext if x<2 a x^2-b x+3 ext if 2 leq x<3 2 x-a+b ext if x geq 3 endarray ight. ]$

Added by Allan H.

Calculus Early Transcendentals

James Stewart 7th Edition

Chapter 2

Instant Answer

Solved by Expert Lucas Finney

04/29/2022

Step 1

For this, the limit of the function as x approaches 2 from the left should be equal to the value of the function at x = 2. The limit of the function as x approaches 2 from the left is given by the first piece of the function, which simplifies to x + 2. So, the Show more…

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