SOLUTION: Please help me solve this equation: Evaluate the following limits or explain why they do not exist. a. {{{ lim(x->0, cotx(1-cosx) ) }}} b. {{{ lim (x->0, (sinx)^tanx ) }}}

Question 363622: Please help me solve this equation:
Evaluate the following limits or explain why they do not exist.
a.
b.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
a.
=* = 1*0 = 0. The second limit was obtained by applying LHopital's rule.
b. Let . then . The limit as x approaches 0 has the form , so apply the LH rule. The new expression becomes AMP Parsing Error of [(cosx/sinx)/(-csc^2x)]: Invalid function '\x)': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. . . Simplifying this, we get . As x goes to 0, -sinx*cosx approaches 0. Hence, lny approaches 0 as x approaches 0, and thus y approaches 1.

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