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Continuity & Differentiability · Question 2 of 125

Question 2

EasyOriginal question

For f(x)={4x−1,x<3x2,x≥3f(x) = \begin{cases} 4x - 1, & x < 3 \\ x^{2}, & x \ge 3 \end{cases}, what is the left-hand limit at x=3x = 3?

Options for question 2

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The left-hand limit uses the piece for xx below 3.

  2. That piece tends to 1111.

Worth noting

9 is the right-hand piece at 3; the left limit uses 4x−14x - 1.

Concept
A one-sided limit
Typical time
60 s
Your time
—
The rule this testsContinuity at a point
Practise this chapter →

Ten questions from Continuity & Differentiability, at your own pace.

Practise this chapter →

Ten questions from Continuity & Differentiability, at your own pace.