Question

The following expansion can be used to find the difficult limits easily. We recommend you to remember them.

$1)e^x=\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+......$

$2\left)ln\right(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}.....,$ -1 < x $\ge$ 1

$3)sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}.....$

$4)cosx=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}......$

$5)tanx=x+\frac{x^3}{3!}+\frac{2x^5}{15!}......$

$6)a^x=1+(lna)x+(lna{)}^2\frac{x^2}{2!}.......$

We will be using these expansions to solve problems in this topic.

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