Find the value of k if lim(x tends to 0) kx cosecx = lim(x tends to 0) x cosec(kx)

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Find the value of k if lim(x tends to 0) kx cosecx = lim(x tends
to 0) x cosec(kx)

Priyanka Kedia · Accepted Answer

Dear Student,

limx→0 kx cosecx=limx→0 x coseckx⇒klimx→0 xcosecx=limx→0 x coseckx⇒klimx→0xsinx=limx→0xsinkx⇒k×1=limx→0xsinkx⇒k=limx→0ddxxddxsinkx      00 form, using L-Hospital's Rule⇒k=limx→01k coskx⇒k=1klimx→01coskx⇒k=1k1cos0⇒k=1k×1⇒k2=1⇒k=±1

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