Does this limit exist? Show steps

Yes, the limit does exist.

Step-by-step explanation:

By definition, a limit in the form:

Exists if and only if:

We are given the limit:

So, in order to prove that this limit exists, we simply have to show that:

Let's do the left-hand side first. We can factor the function:

Simplify:

By direct substitution:

Now, we can evaluate the right-hand side. Again, factor:

Simplify:

And by direct substitution:

Since both the left- and right-hand limits equal 5/4, our original limit does indeed exist.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.