Limit Detective: Product and Quotient Rules

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A limit puzzle using product and quotient rules.

Créé par

Keith benedict Avila

Philippines

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Limit Detective: Product and Quotient RulesVersion en ligne A limit puzzle using product and quotient rules. par Keith benedict Avila 1 As x approaches 1, I’m the limit of (x^2 - 1) divided by (x - 1). What am I? Hints 1 Recognize the remaining expression is x+1, so at x = 1 it equals 2. 2 Cancel the common factor (x-1) and then substitute x = 1. 3 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 1 The result is the product of the two limits. 2 Requires the limits of both functions at the point to exist. 3 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 1 G(a) must not be zero at the limit point. 2 Uses derivatives of numerator and denominator. 3 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 1 Knowing continuity or existance of limits at a is helpful. 2 They let you break complex expressions into simpler parts. 3 These laws cover combining limits of f and g.

Limit Detective: Product and Quotient RulesVersion en ligne

A limit puzzle using product and quotient rules.

par Keith benedict Avila

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).

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.

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.

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.

Vous pouvez intégrer le jeu dans un LMS compatible avec LTI 1.1 ou LTI 1.3 comme Canvas, Moodle ou Blackboard. Les scores seront ainsi automatiquement enregistrés dans le carnet de notes de la plateforme.

Limit Detective: Product and Quotient Rules

Devinette

À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

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Limit Detective: Product and Quotient RulesVersion en ligne

par Keith benedict Avila

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

Hints

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

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

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

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