Calculus

Limits of Functions

One-Sided Limits

         

If f(x)f(x) is the function f(x)={x+10 if x2,2x2 if x>2,f(x)= \begin{cases} -x+10 & \text{ if } \lvert{x}\rvert \leq 2, \\ 2x^2 & \text{ if } \lvert{x}\rvert > 2, \end{cases} what is limx2+f(x)?\displaystyle \lim_{x \to 2^+} f(x)?

What is the value of

limx3x21x2? \lim_{x \to 3^-} \frac{x^2 - 1}{x-2}?

Find the limit of

limx1+x2+xx+1. \lim_{x \to -1^+} \frac{x^2+x}{ |x+1| }.

What is the value of limx0+4xxlimx04xx?\lim_{x \to 0^+} \frac{\lvert{4x}\rvert}{x}-\lim_{x \to 0^-} \frac{\lvert{4x}\rvert}{x}?

What is the value of

limx3+x3? \lim_{x \to 3^+} \sqrt{x-3} ?

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