Find the indicated limit.

lim *t*→2 (6*t*2 − 3*t* + 1)

To find the limit of the given function as \( t \to 2 \):

\[
\lim_{t \to 2} (6t^2 - 3t + 1)
\]

We can substitute \( t = 2 \) directly into the expression, since the function is a polynomial and continuous everywhere.

\[
6(2)^2 - 3(2) + 1 = 6(4) - 6 + 1 = 24 - 6 + 1 = 19
\]

Thus, the limit is:

\[
\lim_{t \to 2} (6t^2 - 3t + 1) = 19
\]

Would you like a more detailed explanation or have any questions?

Here are five related questions for further practice:
1. What is \( \lim_{t \to 3} (5t^2 - 2t + 4) \)?
2. How would you evaluate \( \lim_{x \to -1} (x^3 + 4x^2 - x + 6) \)?
3. What is the limit of \( \lim_{x \to 0} (2x^2 - 3x + 1) \)?
4. Can you compute \( \lim_{t \to 5} (3t^2 + 7t - 2) \)?
5. How do you find \( \lim_{x \to 2} (4x^3 - 2x + 3) \)?

**Tip:** Polynomials are continuous everywhere, so direct substitution is a valid method for finding limits involving polynomials.

Find the indicated limit.

lim t→2 (6t^2 − 3t + 1)

Learn how to calculate the limit of the polynomial function lim t→2 (6t^2 − 3t + 1) using direct substitution. This solution covers key concepts such as polynomial continuity and direct substitution for limits. Suitable for students in Grades 10-12.

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