*Notes to a video lecture on http://www.unizor.com*

__Function Limit - Exercise__

(

(

*x→a*)Try to do these exercises yourself.

All function limits below are supposed to be calculated as argument

**tends to real number**

*x***.**

*a*In other words, we say that

**as**

*f(x)→L***, if**

*x→a***∀**positive

**(however small)**

*ε***∃**

*δ*: (|*x−a*| ≤*δ*) ⇒ (|*f(x)−L*| ≤*ε*)1. If

**is a point of**

*x=a**continuity*for function

**then, as follows from the definition of**

*f(x)**continuous function*,

*f(x) → f(a)*Find the following limits:

**as**

*3x³-2x²+x-1*

*x→1***as**

*2*^{x}

*x→3***as**

*sin(x)*

*x→π/2***as**

*lg(10x)*

*x→100*2. Indeterminate

*0/0*or

*0·∞*

**as**

*(x²−4)/(x−2)*

*x→2***as**

*(1−cos(x))/x²*

*x→0***as**

*(5*]/^{x}−1)*x*

*x→0***as**

*sin(x)/(e*^{x}−1)

*x→0*3. Indeterminate

*∞−∞*

**as**

*sin(x)·tan(x) − sec(x)*

*x→π/2*

*1/(x²-3x+2) − 1/(x²+5x−6)*as

*x→1***as**

*ln(sin(x)) − ln(x)*

*x→0*

*√x+1/(x−4) − √x+16/(2x−8)*as

*x→4*
## No comments:

Post a Comment