Home > Calculus > Determining One Sided Limits

How do you find the limit of #(x+3)^2007# as #x->-4#?

Answer 1

William Abdalla

# lim_(x rarr -4) (x+3)^2007= -1 #

Let #f(x)=(x+3)^2007#,

Then #f(x)# is a continuous function so,

#lim_(x rarr c)=f(c) AA c in RR#

# :. lim_(x rarr -4) f(x) = f(-1) = (-1)^2007 #

Now #(-1)^(2n) = +1#, and #(-1)^(2n+1) = -1 AA n in NN#

Hence #(-1)^2007 = -1#, and so:

# lim_(x rarr -4) (x+3)^2007= -1 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

William Abdalla

To find the limit of (x+3)^2007 as x approaches -4, we can substitute -4 into the expression and evaluate it.

((-4)+3)^2007 = (-1)^2007 = -1

By signing up, you agree to our Terms of Service and Privacy Policy

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.

How do you find the limit of #(x+3)^2007# as #x-&gt;-4#?

How do you find the limit of #(x+3)^2007# as #x->-4#?