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Limit Detective: Product and Quotient Rules

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Limit Detective: Product and Quotient Rules

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About this activity

A limit puzzle using product and quotient rules.

Created by

Keith benedict Avila
Keith benedict Avila
Philippines

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Limit Detective: Product and Quotient Rules
 

Limit Detective: Product and Quotient RulesOnline version

A limit puzzle using product and quotient rules.

by Keith benedict Avila
1

As x approaches 1, I’m the limit of (x^2 - 1) divided by (x - 1). What am I?

Hints

Recognize the remaining expression is x+1, so at x = 1 it equals 2.

Cancel the common factor (x-1) and then substitute x = 1.

Factor the numerator as a difference of squares: (x-1)(x+1).

2

I handle the way two changing things multiply as they approach a point. What rule tells us that lim x->a f(x)g(x) = f(a)g(a) when both f and g settle nicely at a?

Hints

The result is the product of the two limits.

Requires the limits of both functions at the point to exist.

Involves multiplying two functions.

3

When a single thing is on top and another on bottom, their changing rates combine to form a new rate. Which rule gives lim x->a f(x)/g(x) via (f'g - fg')/g^2?

Hints

G(a) must not be zero at the limit point.

Uses derivatives of numerator and denominator.

It's about division of functions.

4

Consider applying limit laws to simple expressions: sums, products, and quotients of limits. Which broad set of rules helps you evaluate these without redoing the entire process?

Hints

Knowing continuity or existance of limits at a is helpful.

They let you break complex expressions into simpler parts.

These laws cover combining limits of f and g.

 
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