1. ## Homework Help

I have two problems that I need to know how to do step by step. Thanks in advance for the help.

1) How do you evaluate the following integral as an infinite series?
∫ [(cos (x^2) - 1) / x] dx

2) How do I find the line tangent to x=ln(t), y=(1+t^2) at t=1?

2. for the first, use the Taylor Series for cosine and insert x^2
then subtract 1 and divide every term by x.

3. This is not a homework service. Please read the forum rules. Rule No. 6

4. It's not graded on correctness. It's just a review assignment to help prepare for an exam which is why I wanted a step by step.

5. Then do what matheagle suggested. Of course the last step is to integrate term by term.

For 2, $\displaystyle \frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$.

6. Originally Posted by fredflintstone

2) How do I find the line tangent to x=ln(t), y=(1+t^2) at t=1?
It passes through $\displaystyle x=0,\ y=2$, and its slope is:

$\displaystyle \dfrac{dy}{dx}=\dfrac{dy}{dt}\dfrac{dt}{dx}$

evaluated at $\displaystyle x=0,\ y=2$.

CB