Questions: Guess f(a) and lim as x approaches a of f(x)

Transcript text: Guess $f(a)$ and $\lim _{x \rightarrow a} f(x)$

Solution

Solution Steps

Step 1: Calculate f(1)

Given $f(x) = x^2 + 1$, we substitute $x = 1$ into the function: $f(1) = (1)^2 + 1 = 1 + 1 = 2$.

Step 2: Calculate $\lim_{x \to 1} f(x)$

Since $f(x)$ is a polynomial function, it is continuous everywhere. Therefore, the limit as $x$ approaches 1 is simply the value of the function at $x = 1$: $\lim_{x \to 1} f(x) = f(1) = 2$.

Final Answer

$f(1) = \boxed{2}$ $\lim_{x \to 1} f(x) = \boxed{2}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >