Question

lim x-> pi/2+ (4/x)secx

Answer 1

Because denominator doesn't approach to 0, you can apply quoient rule.

Then try to evaluate \(\lim_{x\to\frac\pi2^+}~ \sec x\)

Answer 2

Is the quotient rule where you divide by limits?

If so, would I then write lim4/limx *limsecx

Answer 3

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

Answer 4

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?

Answer 5

It approaches -infinity.

Answer 6

Right. and denominator will be just positive value

So anything positive multiplied by negative infinity is just negative infinity. Is that clear?

Answer 7

Answer is \(\boxed{-\infty}\)

Answer 8

Thanks!