Question

evaluate the trigonometric limit
lim csc8t/
t-> 0 csc4t

Answer 1

Use L hospital rule as this is infinity / infinity form

Answer 2

take der of numerator and denominator separately

Answer 3

or rewrite this as 1/sin8t as numeraotr
and 1/sin 4t as denominator

Answer 4

then it changes to sin 4t / sin 8t , now use L hospitals rule and take derivative

Answer 5

i havent been taught the L hospital rule. How is that done? && i rewrote it but i do not know how to solve it from sin4t/sin8t.

Answer 6

ok so now if you put 0 in numerator and deno , it is 0/0 form
meaning we need Hospitals rule
take DER OF NUM separately and also for DEN .

(sin 4t )'= 4cos4t
(sin8t)'=8cost8t

\[\lim_{x \rightarrow 0} \frac{ 4\cos4t }{ 8\cos8t }\]

Answer 7

put t=0

Answer 8

giving 4/8=0.5

Answer 9

does it make sense ?

Answer 10

yes thank you very much