Question

1. the input values increase without bound

graph of h(x)

1. limit statement: x→ lim h(x)=

Explanation:

Step1: Analyze the limit as x increases

We are considering the case when the input values (x - values) increase without bound, i.e., $x
ightarrow+\infty$. Looking at the graph of $h(x)$, as $x$ gets larger and larger in the positive - direction, the function $h(x)$ approaches the line $y = x$.

Step2: Determine the limit value

As $x
ightarrow+\infty$, the function $h(x)$ seems to grow linearly and approaches the line $y = x$. So, $\lim_{x
ightarrow+\infty}h(x)=+\infty$.

Answer:

$\lim_{x
ightarrow+\infty}h(x)=+\infty$