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

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Answer 1 · 2016-12-21T14:27:06

#-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!