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lim-x-1-sec-pi-2-x-arctanx-pi-4-




Question Number 215667 by mathlove last updated on 14/Jan/25
lim_(x→1) sec((π/2)x)(arctanx−(π/4))=?
limx1sec(π2x)(arctanxπ4)=?
Answered by issac last updated on 14/Jan/25
sec((π/2))(arctan(1)−(π/4))
sec(π2)(arctan(1)π4)
Commented by Ghisom last updated on 14/Jan/25
just tell us the value of sec (π/2)
justtellusthevalueofsecπ2
Commented by mathlove last updated on 14/Jan/25
corect answer is −(1/π)
corectansweris1π
Answered by Ghisom last updated on 14/Jan/25
lim_(x→1)  (arctan x −(π/4))sec ((πx)/2) =  =lim_(x→1)  ((arctan x −(π/4))/(cos ((πx)/2))) =       [l′Ho^� pital]  =lim_(x→1)  ((1/(x^2 +1))/(−(π/2)sin ((πx)/2))) =((1/2)/(−(π/2)))=−(1/π)
limx1(arctanxπ4)secπx2==limx1arctanxπ4cosπx2=[lHopital^]=limx11x2+1π2sinπx2=12π2=1π

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