Question

Find lim _{x-->} h(x), if it exists.f(x)=8 x^{2}+2 x+6
(a) h(x)={f(x)} / {x}

Answer 1

To find the limit of h(x) as x approaches a certain value, substitute the expression for f(x) into the expression for h(x), simplify the expression, and evaluate the limit as x approaches the given value.

Step-by-step explanation:

To find the limit of h(x) as x approaches a certain value, we need to evaluate the expression f(x)/x as x gets closer and closer to that value.

1. First, substitute the given expression for f(x) into the expression for h(x): h(x) = (8x^2 + 2x + 6)/x.
2. Simplify the expression by dividing each term in the numerator by x: h(x) = 8x + 2 + 6/x.
3. As x approaches a certain value, the term 6/x becomes smaller and smaller, approaching 0. Thus, the limit of h(x) as x approaches a certain value will be equal to 8x + 2.