Understanding Limits in Differential Calculus: Leibniz and Newton, Exercises of Mathematics

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Differential Calculus (Limit)

Gottfried Wilhelm Leibniz (1646-1716) German Mathematician Sir Isaac Newton (1642 -1726) English physicist and mathematician

To demonstrate how to calculate the limit of a function.

x  a   f (x)  L   f x L x a   lim ( )

Lim g(x Lim f(x) ] g(x) f(x) Lim [ Lim[f(x)g(x)] Lim f(x) Lim g(x) Lim[f(x) g(x)] Lim f(x) Lim g(x) Lim[f(x) g(x)] Lim f(x) Lim g(x) x a x a x a x a x a x a x a x a x a x a x a x a             

2 2 2 2 2 1

1. Evaluatethe limit     x x x x Lt x x x x Lt

2. Evaluatethe limit

sin

If so,find the value

4. Does the followinglimit exist?

3. Show that

2 2

x

x

x π

Lt

x

x

Lt

x

^ 



. x x Lt x x Lt x x           tan 1 sin 1

. 1 cos

Find the value of the followings - 0 2 0

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