How do you find the limit of #tan^2x/x# as #x->0#?

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Answer 1 · 2016-11-24T22:46:34

# lim_(x rarr 0)tan^2x/x = 0 #

# lim_(x rarr 0)tan^2x/x = lim_(x rarr 0)(tanxtanx)/x #

# :. lim_(x rarr 0)tan^2x/x = lim_(x rarr 0)sinx/cosx * sinx/cosx *1/x #

# :. lim_(x rarr 0)tan^2x/x = lim_(x rarr 0)sinx/x * 1/cos^2x * sinx #

# :. lim_(x rarr 0)tan^2x/x = lim_(x rarr 0)sinx/x * lim_(x rarr 0)1/cos^2x * lim_(x rarr 0)sinx #

# :. lim_(x rarr 0)tan^2x/x = lim_(x rarr 0)sinx/x * (1/(lim_(x rarr 0)cos^2x))^2 * lim_(x rarr 0)sinx #

# lim_(x rarr 0)sinx/x =0 # is standard calculus limit

# :. lim_(x rarr 0)tan^2x/x = 0 * 1 ^2* 0 = 0 #