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 2 years ago
Use the definition of continuity to find the constant such that the function is continuous
f(x) = x+3, x<1
2xc, x>1
 2 years ago
Use the definition of continuity to find the constant such that the function is continuous f(x) = x+3, x<1 2xc, x>1

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pasta
 2 years ago
Best ResponseYou've already chosen the best response.1FOR A FUNCTION TO BE CONTINUOS, THE LIMIT AS x TENDS TO 1 FROM THE LEFT MUST BE EQUAL TO THE LIMIT AS x TENDS TO 1 FROM THE POSITIVE DIRECTION. the limit when x<1 is 2 and the limit when x>1 is 2c , the function can only be continuos if the two are equal so we equate them 2=2c c=4 the constant must be 4 so for the function to be continuos, we redefine it to look like f(x)=x+3.x<1 2x+4, x>1

AbbasBagwala
 2 years ago
Best ResponseYou've already chosen the best response.0For a function (line of curve) to be continuous at a point, the limit to the point from both the sides have to be equal. For example, this is a continuous function dw:1349597541245:dw and this is not dw:1349597628198:dw Coming to your problem, if we want your function to be continuous X > 1 from right has to be equal to X> 1 from the left X + 3 = 2X  C Here, X= 1 There for 1 + 3 = 2 (1)  C 2 = 2  C Therefore, C = 4 So, the function is redefined as f(x)=x+3. x < 1 2x+4, x > 1

pasta
 2 years ago
Best ResponseYou've already chosen the best response.1AbbasBagwala .fellow mathmatician your 1st curve looks like a REMOVABLE DISCONTINUITY CURVE
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