# Homework Help: Basic limits

1. Jun 17, 2017

### Tanishq Nandan

1. The problem statement, all variables and given/known data

Find limit for x tending to infinity of: (e^(x^-2)-1)/(2arctan(x^2) - pi)
2. Relevant equations
arctanx +arccotx=pi/2
arctanx=arccot(1/x)

3. The attempt at a solution

P.S I haven't written limit before each step, and hope you can get how I arrived at the first step.I just took 2 common from the denominator and used simple inverse trig.

Where am I going wrong?

2. Jun 17, 2017

### Math_QED

$\frac{1}{\cot^{-1}(x^2)} = \tan^{-1}(x^2)$ is not true.

I didn't check whether you made other mistakes though.

3. Jun 17, 2017

### Staff: Mentor

Do you know L'Hopital's Rule?

4. Jun 18, 2017

### Tanishq Nandan

Ok

5. Jun 18, 2017

### Tanishq Nandan

Yes,I do

6. Jun 18, 2017

### Tanishq Nandan

Ok,I got where I am going wrong,but how to go right?
It looks like we won't be able to use inverse trig

7. Jun 18, 2017

### Math_QED

Use l'Hopital's rule on the first step you wrote down and you should be fine.

8. Jun 18, 2017

### SammyS

Staff Emeritus
Can you find the derivative of $\ \tan^{-1}(x^2) - \frac \pi 2 \,,\$ and derivative of $\ e^{1/x^2}-1\,?$

9. Jun 19, 2017

### Tanishq Nandan

Yeah,I can..and I did,thanks

10. Jun 19, 2017

### Math_QED

Did you get the right answer?

11. Jun 19, 2017

### Tanishq Nandan

Yep,-1/2 (I used another inverse property in b/w though,I had gone wrong in writing the last step,that way I didn't need l'hospital)