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Evaluating Limits Analytically

Total questions: 12

Worksheet time: 20mins

Name
Class
Date
1.

 lim⁡x→1x3+3x2−2x\lim_{x\rightarrow1}^{ }x^3+3x^2-2x  



(a)  

2.

 lim⁡x→−3x2+4x+3x2−3\lim_{x\rightarrow-3}\frac{x^2+4x+3}{x^2-3}  



(a)  

3.

 lim⁡x→−2(x−6)23\lim_{x\rightarrow-2}\left(x-6\right)^{\frac{2}{3}}  



(a)  

4.

 lim⁡x→1x−1x2−1\lim_{x\rightarrow1}\frac{x-1}{x^2-1}  



(a)  

5.

 lim⁡x→01x2\lim_{x\rightarrow0}\frac{1}{x^2}  (you can write the solution as a word)



(a)  

6.

 lim⁡x→2x2+5x+6x+2\lim_{x\rightarrow2}\frac{x^2+5x+6}{x+2}  



(a)  

7.

 lim⁡x→2x2−3x+2x2−4\lim_{x\rightarrow2}\frac{x^2-3x+2}{x^2-4}  



(a)  

8.

 lim⁡x→0(4+x)2−16x\lim_{x\rightarrow0}\frac{\left(4+x\right)^2-16}{x}  



(a)  

9.

 lim⁡x→05x3+8x23x4+12x2\lim_{x\rightarrow0}\frac{5x^3+8x^2}{3x^4+12x^2}  



(a)  

10.

 lim⁡x→πtan⁡xcos⁡x\lim_{x\rightarrow\pi}\frac{\tan x}{\cos x}  



(a)  

11.

 lim⁡x→0x+4−2x\lim_{x\rightarrow0}\frac{\sqrt{x+4}-2}{x}  



(a)  

12.

 lim⁡x→8(x−9)216\lim_{x\rightarrow8}\left(x-9\right)^{216}  



(a)