Let {{MATH_8}}. The domain of {{MATH_9}} is {{MATH_10}}. {{CMD_11}} {{CMD_12}} {{CMD_13}}{{MATH_14}} is not everywhere continuous on {{MATH_15}}{{CMD_16}} {{CMD_17}}{{MATH_18}} is continuous on {{MATH_19}} for some {{MATH_20}}{{CMD_21}} {{CMD_22}}There is some {{MATH_23}} such that {{MATH_24}} is not continuous on {{MATH_25}}.{{CMD_26}} {{CMD_27}}{{MATH_28}} is nowhere continuous on {{MATH_29}}{{CMD_30}} {{CMD_31}}{{MATH_32}} is continuous on {{MATH_33}} for every {{MATH_34}}.{{CMD_35}} {{CMD_36}}{{MATH_37}} is continuous on {{MATH_38}}{{CMD_39}} {{CMD_40}} {{CMD_41}} The preceding statements regarding {{MATH_42}} are true because {{CMD_43}} {{CMD_44}}{{MATH_45}} is the product of two functions whose intervals of continuity have union equal to {{MATH_46}}.{{CMD_47}} {{CMD_48}}the natural logarithm is not continuous.{{CMD_49}} {{CMD_50}}the limit {{MATH_51}} exists and is equal to {{MATH_52}}.{{CMD_53}} {{CMD_54}}{{MATH_55}} is the product of two functions which are continuous on {{MATH_56}}.{{CMD_57}} {{CMD_58}} {{CMD_59}} Next, we shall classify the critical points of {{MATH_60}}.