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Calculus problem, Limits?
What is the first step to this problem?
I can't verify any step I take with a calculator because I know the calculator will calculate undefined if I try to.
Do I do multiply (x-7) top and bottom?
or make (3/x) - (3/7) into (3-3)/7 then shift the 3-3 to the bottom so it would be
(x-7)/(x-7)+(3-3)
3 Answers
- 7 years agoFavorite Answer
First, find a common denominator for the fractions on the top to combine them. That common denominator would be 7x.
Fractions combined on top: (21-3x / 7x)
You can also write the numerator as (-3(x-7))
Multiply the numerator and the denominator of the entire problem by 1 / 7x. This gives you
(-3(x-7)) / 7x(x-7)
Cancel out the (x-7) from the top and bottom and you're left with (-3 / 7x)
Substitute 7 in for X and you get -3/49
The limit as x approaches 7 is -3/49
Source(s): You can check your answer through Wolfram - Rita the dogLv 77 years ago
The fraction simplifies to -3/(7x) as long as x is not 7. So try letting x approach 7 in that.
- ?Lv 77 years ago
Well,
we have :
f(x) = (3/x - 3/7)(x-7)
= 3(1/x - 1/7)/(x-7)
= 3(7-x)/(x-7) * 1/(7x)
= -3/(7x)
therefore :
lim ( x---> 7) f(x) = -3/49
hope it' ll help !!
