## Littlebird one year ago lim x-> pi/2+ (4/x)secx

1. geerky42

Because denominator doesn't approach to 0, you can apply quoient rule. Then try to evaluate $$\lim_{x\to\frac\pi2^+}~ \sec x$$

2. Littlebird

Is the quotient rule where you divide by limits? If so, would I then write lim4/limx *limsecx

3. Littlebird

I think secx = 1/cosx, and cos(pi/2) = 0, but I then I'm stuck

4. geerky42

Yeah. I was more look of $$\dfrac4x\sec x = \dfrac{4\sec x}x$$, so $$\lim\dfrac{4\sec x}x = \dfrac{\lim 4\sec x}{\lim x}$$ Try imagine the graph of sec x, what happen to sec x as x approaches $$\pi/2$$ from right side?

5. Littlebird

It approaches -infinity.

6. geerky42

Right. and denominator will be just positive value So anything positive multiplied by negative infinity is just negative infinity. Is that clear?

7. geerky42

Answer is $$\boxed{-\infty}$$

8. Littlebird

Thanks!