Limit of a Function: Definition, Solved Problems

Let us definite the limit of a function. Let f(x) be a function of x, and let a be a real number. We say limx→a f(x) = L if both the left hand and the right hand limit of f(x) exist and equal. That is,

limx→a- f(x) = limx→a+ f(x) = L.

For example, limx→1 x2 = 12 = 1.

Solved Problems on Limits

limx→0 sinx/x

limx→0 cosx/x

limx→0 tanx/x

limx→0 xsin(1/x)

limx→0 x2sin(1/x)

limx→0 (1-cosx)/x2

limx→1 (xn-1)/(x-1)

limx→a (xn-an)/(x-a)

limx→∞ sinx/x

limx→∞ cosx/x

limx→∞ tanx/x

limx→∞ 1/x2

limx→∞ x1/x

Limit of (1+$\frac{1}{x}$)x when x→∞

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