Math1011_Week04_26_27

# Math1011_Week04_26_27 - Math1011 Learning Strategies Center...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math1011 - Learning Strategies Center 9/23/2009 Find the limits 2 1 lim x x → | | lim x x x → 1 lim x x → 1 lim x x → ∞ lim cos x x → ∞ lim 5 x x − → ∞ 5 3.5 h h Simplify: 1/6 h h Simplify: Math1011 - Learning Strategies Center 9/23/2009 2 1 lim x x → 2 1 lim x x → = ∞ | | lim x x x → | | | | | | | | | | lim lim 1 lim lim 1 lim , lim DNE x x x x x x x x x x x x x x x x x x x x x → − → − − → + → + − → − → + → = = − = = ≠ As lim 1 lim x x → 1 lim x x → DNE (limit right ≠ limit left) 1 lim x x → ∞ 1 lim x x → ∞ = lim cos x x → ∞ lim cos (oscillates between -1 and 1) x x D N E → ∞ lim 5 x x − → ∞ 1 1 5 lim x ∞ ∞ → ∞ = = 5 3.5 h h Simplify: 5 3.5 5 3.5 1.5 h h h h − = = 1/6 h h Simplify: 1/6 1 (1/6) 5/6 h h h h − = = (Doc #011r.07t) Math1011 Section 2.6 2 Given the graph of ƒ : At what points on the interval [-5, 5] is ƒ discontinuous? Explain by indicating the type of discontinuity. At what points on its domain is ƒ discontinuous? Math1011 Section 2.6 2 Given the graph of ƒ : At what points on the interval [-5, 5] is ƒ discontinuous? Explain by indicating the type of discontinuity. -2 (infinite discontinuity) -1 (removable discontinuity) 1 (jump discontinuity) 3 (removable discontinuity) At what points on its domain is ƒ discontinuous? 1 (jump discontinuity) 3 (removable discontinuity) Note: x = -2 and x = -1 are not included as these points are not in the domain of ƒ. (Doc #011.w.26.01t) Math1011 Section 2.6 3 Sketch the graph of the function and identify the type of discontinuity ƒ (x) has at x = 1. 2 4 3 1 ( ) 1 3 1 x x if x f x x if x ⎧ − + ≠ ⎪ = − ⎨ ⎪ = ⎩ How could we redefine ƒ(x) to make it continuous? Math1011 Section 2.6 3 Sketch the graph of the function and identify the type of discontinuity ƒ (x) has at x = 1. 2 4 3 1 ( ) 1 3 1 x x if x f x x if x ⎧ − + ≠ ⎪ = − ⎨ ⎪ = ⎩ Definition of Continuity A function is continuous at a number a if lim ( ) ( ) x a f x f a → = 2 1 4 3 1 1 ( 1)( 3) 1 1 1 lim ( ) ? (1) lim ? (1) lim ? (1) lim 3 ? (1) 2 3 So, f(x) is not continuous at 1 Removable Discontinuity at x=1 x x x x x x x x x x f x f f f x f → − + − → − − − → → − − ≠ How could we redefine ƒ(x) to make it continuous?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 16

Math1011_Week04_26_27 - Math1011 Learning Strategies Center...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online