Limits

Find the indicated limit, if it exists.  

1. (a) \(\displaystyle{\lim_{x \to -1}  \: 5x^2-4x+15}\)    (b) \(\displaystyle{\lim_{x \to -1}  \frac{2x+1}{x+5}} \)   (c) \(\displaystyle{\lim_{x \to 5}   \:(x^2+2)(x^2-25)}\)  solution

2. (a) \(\displaystyle{\lim_{x \to 1^-} \frac{4-x}{x+2}} \)     (b)  \(\displaystyle{\lim_{x \to -2^+} \frac{x-7}{x+5}} \)   solution

3. \(\displaystyle{\lim_{x \to 0} \frac{x^2+x}{x}} \)      solution 

4.   (a) \(\displaystyle{\lim_{x \to 0} \, \dfrac{x^2-4x}{x^3+3x}}\)           (b) \(\displaystyle{\lim_{x \to 2} \frac{x^2-2x}{x^2-x-2} }\)    solution

5.   (a) \(\displaystyle{\lim_{x \to -1} 5x^3-3x^2+7x-11}\)        (b) \(\displaystyle{\lim_{x \to 3} \frac{x^2-2x-3}{x-3} }\)    solution

6. \(\displaystyle{\lim_{x \to 1} \frac{x^2-1}{x-1}} \)       solution 

7. (a) \( \displaystyle{\lim_{x \to 3^+} \frac{x+1}{x-3}} \)  (b) \( \displaystyle{\lim_{x \to 2^-} \frac{1}{x-2}} \)  solution 

8. \(\displaystyle{\lim_{x \to 3} \frac{x+9}{x-3}} \)   solution1      solution2

9. \(\displaystyle{\lim_{x \to -1} \frac{x^2+x}{x^2-x-2}} \)      solution    

10. \(\displaystyle{\lim_{h \rightarrow 0}\: \frac{(2+h)^2-4}{h}} \)      solution  

11. \( \displaystyle{\lim_{x \to \infty} \frac{x^2-5x+7}{4x^2-x^3+1}} \)    solution

12. \( \displaystyle{\lim_{x \to \infty} \frac{3x^4-2x+5}{4x^3-5x+1}}\)       solution 

13. \(\displaystyle{\lim_{x \to \infty} \frac{3x^2-2x+5}{4x^2 + 2x+1}}\)       solution

14. \(\displaystyle{\lim_{x \to -\infty} \frac{1-2x+4x^3}{2+x^2-3x^3}}\)  solution