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Find the values of a and b that make f continuous everywhere. f(x) = egin{cases} frac{x^2 - 4}{x - 2} & ext{if } x < 2\ ax^2 - bx + 3 & ext{if } 2 le x < 3\ 2x - a + b & ext{if } x ge 3 end{cases} a = b = 

          Find the values of a and b that make f continuous everywhere.
f(x) = egin{cases} frac{x^2 - 4}{x - 2} & 	ext{if } x < 2\ ax^2 - bx + 3 & 	ext{if } 2 le x < 3\ 2x - a + b & 	ext{if } x ge 3 end{cases}
a =
b =
Find the values of a and b that make f continuous everywhere. f(x) = egincases fracx^2 - 4x - 2 extif x < 2 ax^2 - bx + 3 extif 2 le x < 3 2x - a + b extif x ge 3 endcases a = b =

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the values of a and b that make f continuous everywhere: if x < 2 f(x) = x - 2 if 2 < x < 3 f(x) = ax^2 + bx + 3 if x > 3 f(x) = 2x - a + b
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Transcript

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00:01 Hi, here in this question we are given that function f of x equals to here x square minus 4, x minus 2, this is when x less than 2 and x ax square minus b plus 3 when 2 less than or equal to x less than 3.
00:21 Again 4x minus a plus b if x is greater than or equal to 3.
00:27 So here we need to check at which point.
00:31 Of a and b, the function is continuous.
00:35 A equals to what and b equals to what.
00:38 Now here, if the function is continuous at 2, then the value of x square minus 4 upon x minus 2 equals to ax square minus bx plus 3.
00:50 So here on further simplification, we have x plus 2 equals to ax square minus bx plus 3...
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