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What is the value of the following limit: #lim_(x-> 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)#?

Answer 1

Ezra Adams

#-1/16#, or choice A.

The notation #f(x)# signifies to put the function into the limit, so:

#=>lim_(x-> 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)#

#=> lim_(x-> 1) ((4 - 1(x + 3))/(4(x + 3)))/( x - 1)#

#=> lim_(x-> 1) ((4 - x - 3)/(4(x + 3)))/(x- 1)#

#=> lim_(x-> 1) ((1 - x)/(4(x +3)))/(x- 1)#

#=> lim_(x-> 1) (1 - x)/(4(x + 3)(x - 1))#

#=> lim_(x->1) -(x -1)/(4(x + 3)(x - 1))#

#=> lim_(x->1) -1/(4(x + 3))#

We can evaluate now:

#=> -1/(4(1 + 3))#

#=> -1/16#

This would be choice A.

Hopefully this helps!

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Answer 2

Christopher Allers

The value of the given limit is -1/8.

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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.

What is the value of the following limit: #lim_(x-&gt; 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)#?

What is the value of the following limit: #lim_(x-> 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)#?