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How do you find the limit of # ((x/4)+3) # as x approaches #6#?

Answer 1

# lim_(x rarr 6) (x/4+3) = 4.5 #

If we define #f(x)=x/4+3#, then #f(x)# is continuous everywhere (ie it is well behaved and it has no jumps, discontinuities or places where the function is not defied).

Consequently

#lim_(x rarr a) f(x) = f(a) # for all values of #a#

hence

#lim_(x rarr 6) (x/4+3) = lim_(x rarr 6) f(x) # # " " = f(6) # # " " = 6/4+3 # # " " = 4.5 #

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Answer 2

Emily Ammerman

To find the limit of ((x/4)+3) as x approaches 6, we substitute 6 into the expression: ((6/4)+3). Simplifying this gives us (3/2+3), which further simplifies to (3/2+6/2). Combining the fractions, we get (9/2). Therefore, the limit of ((x/4)+3) as x approaches 6 is 9/2.

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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.