# How do you find the limit of # 1 / (x-3)# as x approaches 3?

Given,

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To find the limit of 1 / (x-3) as x approaches 3, we can substitute the value of 3 into the expression. However, this would result in division by zero, which is undefined. Therefore, the limit does not exist.

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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.

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.

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.

- Suppose that #lim_(xrarrc) f(x) = 0# and there exists a constant #K# such that #∣g(x)∣ ≤ K " for all " x nec# in some open interval containing c. Show that# lim_(x→c) (f(x)g(x)) = 0#?
- How do you find the limit of #(sinx)/(3x)# as x approaches #oo#?
- How do you find the limit #(x^3+4x+8)/(2x^3-2)# as #x->1^+#?
- How do you evaluate the limit #x/sin(x/2)# as x approaches #0#?
- How do you evaluate #(csc(x) - cot(x))# as x approaches 0?

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