Determining One Sided Limits

Key Questions

• What is a one-sided limit?

  This is when you attempt to evaluate the limit of a function from either the left side or the right side.

  AJ Speller · · Sep 11 2014
• When is a one sided limit undefined?

  A one sided limit does not exist when:

  1.`""` there is a vertical asymptote.

  ex.) `lim_{x to 0^+} 1/x =1/{0^+}=+infty`

  So, the limit does not exist.

  2.`""` there are violent oscillations.

  ex.) `lim_{x to 0^-}sin(1/x)` does not exist

  due to violent oscillations, which looks like:

  ---

  I hope that this was helpful.

  Wataru · 2 · Dec 12 2014

• When is a one sided limit undefined?
• How do you find a one sided limit for an absolute value function?
• How do you find the limit `lim_(x->3^+)|3-x|/(x^2-2x-3)` ?
• How do you find the limit `lim_(x->2^+)sqrt(2-x)` ?
• How do you find the limit `lim_(x->0^-)|x|/x` ?
• How do you find the limit as x approaches 2 of the piecewise function `f(x)={(4-x^2,if x<=2),(x-1,if x>2):}` ?
• How do you find the limit of the piecewise function `f(x)={(x^2,if x text{ is rational}),(0,if xtext{ is irrational}):}` as x approaches 0?
• How do you find one sided limits without graph?
• How do you find one sided limits algebraically?
• How do you determine one sided limits numerically?
• How do you find one sided limits and limits of piecewise functions?
• What is the limit as x approaches 0 from the right-hand side of `ln(x)`?
• How do you find the limit of `(2x-1)/(abs(2x^3 - x^2))` as x is approaching 0.5 from the negative side?
• How do you find the limit of `(x^2-3x+2)/(x^3-4x)` as x approaches 2 from the right, as x approaches -2 from the right, as x approaches 0 from the left, and as x approaches 1 from the right?
• How do you find the limit of `(x+3)/(x-3)` as x approaches 3+?
• How do you find the limit of `1/(x-2)` as x approaches 2 from the left?
• How do you find the limit of `abs(x-4) / (x-4)` x as it approaches 4 from the left and right?
• How do you find the limit of `(1)/(x-2)` x as it approaches 2 from the right?
• What is `lim_(t-> 0) (1/t -1/t^2-t)`?
• What is `lim_ (xrarr0) (1/x -1/x^2-x)`?
• What is `lim_(xrarr4) ([(x^2) + 5x + 4] / [(x^2) + 3x -4])`?
• What is `lim_(xrarroo) ((6x) / e^x)`?
• What is `lim_(xrarroo) sin(1/x)/x`?
• What is `lim_(xrarroo) 1/x`?
• What is `lim_(xrarroo) sin(x)/x`?
• What is `lim_(xrarroo) (e^xsin(1/x))/x`?
• What is `lim_(xrarroo) (e^(2x)sin(1/x))/x^2`?
• What is `lim_(xrarroo) (3x^3+2x+500x-1)/(x^4-8000x^3-30x)`?
• What is `lim_(trarroo) (1/t -1/(t^2+t))`?
• What is `lim_(trarr0) (1/t -1/(t^2+t))`?
• What is `lim_(xrarr-3) (2x+6)/|x+3|`?
• What is `lim_(xrarr-1) (1/x-1)/(x-1)`?
• What is `lim_(xrarr4) ( x^4 -256) / (x^3 - 64)`?
• What is `lim_(xrarr0) ( 9/x-(9x)/(x^2+x))`?
• What is `lim_(xrarr0) ( 1 + 3x )^(1/x)`?
• What is `lim_(xrarr0+) ( x )^(2x)`?
• What is `lim_(xrarr0+)(ln x) / (csc x)`?
• What is `lim_(xrarroo) ( 1 + ( r/x ) ) ^ x`, where r is any real number?
• What is `lim_(xrarroo)(ln(6x+10)-ln(7+3x))`?
• What is `lim_(xrarroo)(ln(9x+10)-ln(2+3x^2))`?
• `lim_(trarr1){t-1}/(t^3-1)=` ?
• Question #e27b8
• Question #e5c7f
• Find the solutions `x > 0 in RR` for `2^x + 2^(1+1/sqrt(x))=6`?
• What is the `lim_{t->0} 1/(t sqrt(1+t)) - 1/t`?
• How do you find the limit of `2x+5` as `x->7^-`?
• How do you find the limit of `2x+5` as `x->-oo`?
• How do you find the limit of `(x+3)^2006` as `x->-4`?
• How do you find the limit of `(x+3)^2007` as `x->-4`?
• How do you find the limit of `(x+3)^2007` as `x->-oo`?
• How do you find the limit of `(t^2+t-2)/(t^2-1)` as `t->1`?
• How do you find the limit of `(t^2+t-2)/(t^2-1)` as `t->-1`?
• How do you find the limit of `(x^2+3)/(x^2+4)` as `x->-oo`?
• How do you find the limit of `(x^5+3)/(x^2+4)` as `x->oo`?
• How do you find the limit of `(x^2+1)/(x^5+2))` as `x->oo`?
• How do you find the limit of `(2x+1)^4/(3x^2+1)^2` as `x->oo`?
• How do you find the limit of `(2u+1)^4/(3u^2+1)^2` as `u->oo`?
• How do you find the limit of `(2t+1)^4/(3t^2+1)^2` as `t->0`?
• How do you find the limit of `(sqrtx-3)/(x-9)` as `x->9`?
• How do you find the limit of `(x-5)/(x^2-25)` as `x->5^-`?
• How do you find the limit of `(2-x)/(x^2-4)` as `x->2^+`?
• How do you find the limit of `x/sqrt(x^2-9)` as `x->3^-`?
• How do you find the limit of `(sqrtx-2)/(x-4)` as `x->4^-`?
• How do you find the limit of `absx/x` as `x->2^-`?
• Question #866ae
• Find the solutions of `x^2=2^x`?
• What's the limit of xArctan(x/x^2+1) as x approaches positive infinity ?
• What's the limit of `1/(x-1)arctan(2/(x-1)-pi/2)` as x approaches positive 1 ? Thanks!
• Would you please tell me what's the limit of `(V_n-U_n)` as `n` approaches positive infinity ? PS: `U_(n+1)= sqrt(U_nV_n)` and `V_(n+1)=(U_n+V_n)/2`
• How do you find `lim_(x->0^-)cosx/x`?
• Question #8ada3
• Question #8deff
• Question #3be0a
• Question #a25bb
• Question #747f2
• How do you solve for `x in RR` the equation `x! = e^x` ?
• Find the limit as x approaches 3 from the right `ln(x^2-9)`?
• What is `lim_(x->0) (1-cosx)^2/x` ?
• Evaluate the limit `lim_(x rarr 0^+) (1+1/x)^x`?
• How can I evaluate `lim_(x->0) (sinx-x)/x^3` without using L'Hopital's rule?
• What is `lim_(x->+oo) x/(1-2x)`?