Question

1) For what values of a and b will $f(x) = \begin{cases} \frac{x^2 - 4}{x - 2}, & x < 2\\ ax^2 - bx + 3, & 2 \le x < 3\\ 2x - a + b, & x \ge 3 \end{cases}$ be continuous? Explain your reasoning using the three conditions of continuity. Use one sided limit in your explanation(s).

          1) For what values of a and b will $f(x) = \begin{cases} \frac{x^2 - 4}{x - 2}, & x < 2\\ ax^2 - bx + 3, & 2 \le x < 3\\ 2x - a + b, & x \ge 3 \end{cases}$ be continuous?
Explain your reasoning using the three conditions of continuity. Use one sided limit in your explanation(s).

1) For what values of a and b will f(x) = (x^2 - 4)/(x - 2), x < 2
ax^2 - bx + 3, 2 ≤ x < 3
2x - a + b, x ≥ 3 be continuous?
Explain your reasoning using the three conditions of continuity. Use one sided limit in your explanation(s).

Added by Jesse G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

Step 1

In order for f(x) to be continuous at x = 2, the left-hand limit and the right-hand limit must exist and be equal. To find the left-hand limit, we need to evaluate the expression f(x) as x approaches 2 from the left side. So, we substitute x = 2 - h into the Show more…

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, x < 2 = 2 2) For what values of a and b will f(x) = 2x - a + bx^3 Explain your reasoning using the three conditions of continuity. Use one-sided limits in your explanations. [8 MARKS]