For what value of c is f(x) continuous at x=4? Justify your answer.
If f(x) = {3x^2+5 if x<1
{x^3+2x+5 if 1 ≤ x ≤ 4
{x+c if x>4
If f(x) = {3x^2+5 if x<1
{x^3+2x+5 if 1 ≤ x ≤ 4
{x+c if x>4
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You need to evaluate the limit of f(x) as it approaches 4 from the left
The limit will be 4^3 +2(4) + 5 = 64 + 8 + 5 = 77
Now evaluate the limit of f(x) as it approaches 4 from the right
The limit will be x + c = 4 + c
For f(x) to be continuous at x = 4 these two must be equal to each other (the graph of the function needs to 'join up' at x=4)
4 + c = 77 gives c = 73
Edit: no actual calculus involved, but in can be a preparatory question in a calculus course as you come to understand functions.
The limit will be 4^3 +2(4) + 5 = 64 + 8 + 5 = 77
Now evaluate the limit of f(x) as it approaches 4 from the right
The limit will be x + c = 4 + c
For f(x) to be continuous at x = 4 these two must be equal to each other (the graph of the function needs to 'join up' at x=4)
4 + c = 77 gives c = 73
Edit: no actual calculus involved, but in can be a preparatory question in a calculus course as you come to understand functions.
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this is obviously a trick question! tell your teacher so! extra marks are in order!
much thanks,
aLFREDO
much thanks,
aLFREDO