Evaluation of trigonometric limit when variable tends to non zero term ( algorithm)

Examples based on Evaluation of trigonometric limits.

The value of the limit when x tends to zero of the expression (e^(x)-1)/(x) is

Find trigonometric ratios of angle A in terms of angle A/3?

When is the sum of two non zero vectors is zero ?

Illustration on Trigonometric Limits || 0 || Infinity and change OF Variable

The value of the limit when x tends to zero of the expression (1+x)^((1)/(pi)) is

The value of the limit when x tends to zero of the expression ([(1+x)^(n)-1])/(x) is

The value of the limit when x tends to zero of the expression ((a+x^(2))^((1)/(2))-(a-x^(2))^((1)/(2)))/(x^(2)) is

The value of the limit whenat the limit when x tends to 2 of the expression (x-2)^(-1)-(x^(2)-3x+2)^(-1) is

The value of the limit when n tends to infinity of the expression (1+(1)/(n))^(n) is