Evaluate the left hand and right hand limits of the following functions at x=2. Does lim (x->2) f(x) exists? f(x)=2x+3 if x2

Evaluate the left hand and right hand limits of the following functions at x=2. Does lim (x→2) f(x) exists? f(x)=2x+3 if x<=2 & f(x) = x+5 if x>2

Problem

Question

Evaluate the left hand and right hand limits of the following functions at x=2. Does lim (x→2) f(x) exists? f(x)=2x+3 if x<=2 & f(x) = x+5 if x>2

Topic

Limit and its fundamentals

Problems

1. Evaluate lim x→a ((sqrt(x)+sqrt(a))/(x+a))
2. Find the value of lim x→0 (e^x-1)/x
3. Evaluate lim (x→0) sin nx/x
4. Evaluate lim (x→1) ((sqrt(1+x)-sqrt(1-x))/(1+x))
5. Evaluate lim (n→∞) (1+2+3+…+n)/n^2
6. Evaluate lim (x→0) (e^ (-x)-x-1)/x
7. Evaluate lim (x→5) (e^x-e^5)/(x-5)
8. Show that lim (x→4) |x-4|/(x-4) does not exist
9. Evaluate lim (x→1) ((2x-3) (sqrt(x)-1)) / (2x^2+x-3)
10. Evaluate lim (x→0) tan2x-sin2x /x^3
11. Evaluate lim (x→pi/6) (sqrt(3) sinx-cosx )/(x-pi/6)
12. Evaluate lim (x→0) (log(6+x)-log(6-x))/x
13. Find lim (x→1) f(x), where f(x) = (x^2-1, x≤1 & -x^2-1, x>1)
14. Evaluate lim (x→1) ((x^m-1))/(x^n-1)
15. Find the value of k if lim (x→1) (x^4-1)/(x-1) = lim (x→k) (x^3-k^3)/(x^2-k^2)
16. Find the value of a and b if lim (x→2) f(x) and lim (x→4) f(x) exists where f(x) = x^2+ax+b for 0≤x<2 & 3x+2 for 2≤x≤4 & 2ax+5b, 4<x≤8
17. Evaluate lim (x→0) sec4x-sec2x /sec2x-secx
18. Evaluate lim (x→0) (e^x-e^sinx)/(x-sinx)
19. Evaluate the left hand and right hand limits of the following functions at x=2. Does lim (x→2) f(x) exists? f(x)=2x+3 if x<=2 & f(x) = x+5 if x>2