Limits (Grade 12 NSC Matric Mathematics): Flashcards

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Limits
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What do limits describe?

Value a function approaches as x gets close to a specific value

Read: lim⁡x→af(x)=L\lim_{x \to a} f(x) = L

Limit of f(x) as x approaches a equals L

Limits focus on behaviour where?

Near a point, not necessarily at that exact point

Notation for left-hand limit

lim⁡x→a−f(x)\lim_{x \to a^-} f(x)

Notation for right-hand limit

lim⁡x→a+f(x)\lim_{x \to a^+} f(x)

When does a limit exist?

When both one-sided limits exist and are equal

Formula for gradient at a point

lim⁡h→0f(a+h)−f(a)h\lim_{h \to 0} \frac{f(a + h) - f(a)}{h}

What is a secant line?

Line connecting two points on a curve

What does secant line approach?

Tangent line as points get closer together

How to solve 00\frac{0}{0} form?

Factorise and cancel common terms

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