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Find a value for the constant c so that the function is continuous at x = 7?
(1) c= ????
if f(x) then continuous for ALL real numbers x?
(2) Answer (Y/N): ????
f(x) = c/x-2 if x < 7
5x-1 if x ≥ 7
2 Answers
- WoodsmanLv 71 decade agoFavorite Answer
At x=7, 5x-1=34.
For c/x-2 to approach 34 as x approaches 7, then c must be 252.
If you meant c/(x-2), then c must be 170.
- 1 decade ago
to be continuous the limits have to be the same as they approach 7 at both sides right? just calculate them and put them equal to each other:
approaching 7 from the left = approaching 7 from the right
lim c/x-2= lim 5x-1
x--> 7- x---> 7+ (for linear equations to find limit just plug 7 into the function)
c/7 -2 = 5*7 -1
c/7 = 35-1+2
c= 7* 36 = 252
