Limits (Grade 12 NSC Matric Mathematics): Quizzes

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Limits
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What do limits describe in calculus?

Value a function approaches near a point

How do you read the notation lim⁡x→3f(x)=7\lim_{x \to 3} f(x) = 7?

Limit of f(x)f(x) as xx approaches 33 is 77

What is lim⁡x→510\lim_{x \to 5} 10?

1010

What is lim⁡x→2(x+4)\lim_{x \to 2} (x + 4)?

66

When does a limit exist at a point?

When both one-sided limits are equal

What is lim⁡x→10x2−100x−10\lim_{x \to 10} \frac{x^2 - 100}{x - 10}?

2020

What formula gives the gradient at a point?

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

For g(x)=3x2g(x) = 3x^2, what is the gradient at x=−1x = -1?

−6-6

What happens as a secant line's two points get closer?

Secant line approaches the tangent line

What should you check first when evaluating limits?

If direct substitution works

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