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How do you prove that the function #1/x# is continuous at x=1?

Answer 1

Christopher Allers

See the Explanation.

To prove that a fun. #F(x)# is continuous (cont.) at

#x=a, a in D_F"=the Domain of "F#, we have to prove that,

#lim_(xrarra) F(x)=F(a)#.

So, in our case, we have,

#lim_(xrarr1) f(x)#

#=lim_(xrarr1) 1/x#

#=1/1=1#.

#f(1)=1#.

Thus, #lim_(xrarr1) f(x)=f(1)#.

Hence, #f# is cont. at #x=1#.

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Answer 2

Elijah Abram

To prove that the function 1/x is continuous at x=1, we can use the definition of continuity. A function is continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.

In this case, we need to evaluate the limit of 1/x as x approaches 1.

lim(x→1) 1/x = 1/1 = 1

Since the limit of 1/x as x approaches 1 is equal to 1, and the value of the function at x=1 is also 1, we can conclude that the function 1/x is continuous at x=1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.