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Longhand

Before the midterm

Stopping at ‘does not exist’ when the limit is +∞ or −∞

The habit: When the values grow without bound with one sign, the limit is not a number, but write +∞ or −∞: that says how it fails, and it is the answer asked for.

4 practice questions are built to catch it, in 2 topics.

Practise against it: 3 questions

What it looks like

A question from limits, with the answer this slip gives beside the right one.

Introductory1 mark · 2 min

Evaluate the one-sided limit.

lim⁡x→4+x+24−x\lim_{x \to 4^{+}} \frac{x + 2}{4 - x}
With the slip
The limit does not exist
Worked through
−∞\displaystyle -\infty

The values grow without bound in size, all with one sign, and that has a name: ∞, signed like the values.

See the worked solution

Where it comes up

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

  1. 01
    Evaluate the limit. lim⁡x→−3x−1(x+3)2\displaystyle \lim_{x \to -3} \frac{x - 1}{(x + 3)^{2}}

    LimitsIntroductory

  2. 02
    The graph of a function hh is shown, with dashed asymptotes at x=−2x = -2 and y=1y = 1. Use it to find the one-sided limit below. lim⁡x→−2+h(x)\displaystyle \lim_{x \to -2^{+}} h(x)

    ContinuityIntroductory

  3. 03
    Two students evaluate the one-sided limit lim⁡x→−2+x2+x−2x2+4x+4\displaystyle\lim_{x \to -2^{+}} \frac{x^{2} + x - 2}{x^{2} + 4x + 4} as shown. Which solution is right, and why?

    LimitsChallenging

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