Rutgers - Calculus 640 - Class Notes - Week 3

View Full Material##### School: Rutgers University

##### Department: Calculus and Pre Calculus

##### Course: Calculus 1

##### Term: Spring 2019

##### Tags: IVT, Squeeze Theorem, limits with infinity, asymptotes, and Calculus

##### Name: Week 3 Notes

##### Description: These notes cover from Section 2.4 to Section 2.8

##### Uploaded: 02/13/2019

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Unformatted text preview: Sec 2.4 Contudom 03/05/19 Ex- find ab so that fiscontinuat x>2.- - 3h - X if * > 2 f is Continuous if piecewise, f(x)-1(2). Because fois we need to consider the left/right limits Separately Need: a b So that fim ) - f() = f(2) X-2 im 16) - lim (36 ) lim im (2x2-1) (8) *- * 2(ay- 1 3 -2 <->24 Section 2.5 f(x) hos on indeterminate form of x=ciff of the form; & , , 0.00, 0,09, 09 Ex: Evolvate each lirit 2-3x-101 a) 512-25 Plugging in 5 gives 39 (x+2) x lim5 (x+5) ligos [***] 05 - ToPlugging x -9 din We'll mwply by The O = lim (x-1)(1843) - electron (Tx+3) - 89 +3 - 6 c) Harmony bet -] Mugging in gives most het en die wint z limony [] e coli ] LX+1 Plugging x -1 in gives - This is NOT an indeterminate for s , the valve becomes slase the Smolt positive number Close to - (close to 0) Note: lim. [*] DNE because -=(-1)(x-a) They are a home as a lot]Section 2.6 The Squeeze Theorem. Suppose for to that and in 9) = limhe "Then * f(x) -L (x) = f() sh(*) EL to evoluotel Ex:. Use Squeeze Theoreen the limit hay mo [x2 sin (4) f(x) = x2 sio We need to find 96), h(x). by bounding Stact pool of f(x) Build up to t odding/multiplying /etc other values Multiply by -32x2 siri Then we have By Squeeze Theorem lim x 2 sin ) = Note: - cos X 61 -1 < sin x 1 These are common bounds Theorem. used when applying Squeeze

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