I understand the basicsof trig limits, but of a gamut of 500 questions there are several I just can't get the answer for. What am I doing wrong?
1. Lim (sinx / x+tanx)
2. Lim([cot^2]x / 1-cscx)
3. Lim (tan4x/tan7x)
1. I tend to end up at a mess here: I multiply the top and bottom by 'x' so I can use the sinx/x identity, and ultimately end up with (xcosx/(xcosx+sinx)) and get lost from there. According to the back of the book, the answer is 1/2.
2. Everything I try here just ends up a mess
3. I tend to end up at
(sin4x)/4x . 7x/(sin7x) . 4x/(cos4x) . (cos7x/7x)
=(4/7) . (0) . (undefined)
the answer in the back of the book is 4/7,and I don't know how to get there
Thanks in advance! I have a test Tuesday,and I'm so lost in all of this.