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

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geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Because denominator doesn't approach to 0, you can apply quoient rule. Then try to evaluate \(\lim_{x\to\frac\pi2^+}~ \sec x\)

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0Is the quotient rule where you divide by limits? If so, would I then write lim4/limx *limsecx

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0I think secx = 1/cosx, and cos(pi/2) = 0, but I then I'm stuck

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. 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?

Littlebird
 one year ago
Best ResponseYou've already chosen the best response.0It approaches infinity.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Right. and denominator will be just positive value So anything positive multiplied by negative infinity is just negative infinity. Is that clear?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Answer is \(\boxed{\infty}\)
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