Your list · 0 हिं

Continuity & Differentiability · Question 7 of 125

What is the left-hand limit of this three-piece f at x = 1?

Question 7

EasyOriginal question

$f(x) = x + 1$ for $x < 1$ , $f(1) = 2$ , and $f(x) = 3x - 1$ for $x > 1$ .

What is the left-hand limit of this three-piece $f$ at $x = 1$ ?

0

Correct answerYour answer

1

Correct answerYour answer

2

Correct answerYour answer

3

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

For $x < 1$ , $f(x) = x + 1$ .
As $x \to 1^{-}$ , $x + 1 \to 2$ .

Worth noting

1 is the value of $x$ , not of $x + 1$ .

Concept: A one-sided limit
Typical timeTypical: 90 s
Your timeYours: —

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.

Practise this chapter All 125 questions in Continuity & Differentiability Revise the notes for Continuity & Differentiability