do thick u r smart enogh? solve : lim cot 2x / sin 2x when x goes to zero????????

Question

it simple

Answer 1

Let F(x) = cot 2x / sin 2x.

Since cot A = (cos A) / (sin A), it follows that
cot 2x / sin 2x = (cos 2x) / (sin 2x)^2.

Thus as x approaches 0, cos 2x -> 1 but sin 2x -> 0. Note that the expression in the denominator of a rational expression must not be equal to zero (0).

Alternatively, we consider the left and right hand limit of the function F(x). If it turns out that two limits are the same, then that limit is the value of F(x) as x approaches 0. Otherwise, the limit of F(x) as x approaches 0 does not exists.

For the left-hand limit, we notice that as x approaches from the left of 0 (i.e., x -> 0-), cos 2x -> 1. But, sin 2x -> 0-; that is sin 2x approaches 0 through negative values. Hence,
L1 = limit_{x -> 0-} F(x) = 1 / 0- = -∞.

On the other hand, for the right-hand limit, we observe that x goes from the right of 0 (i.e., x -> 0+), cos 2x -> 1. But, sin 2x -> 0+; that is, sin 2x as approaches 0 through positive values. Hence,
L2 = limit_{x -> 0-} F(x) = 1 / 0+ = +∞.

Since L1 and L2 are not equal, it shows that the limit of F(x) as x approches to 0 does not exists.

Answer 2

its 1

Answer 3

Consider cot 2x / sin 2x = cos 2x / sin^2 2x
taking the limit it is now apparent that it diverges to infinity since cos 0 =1, and sin 0 = 0

Answer 4

"i don't prefer to unravel for the zeros. i prefer to locate a cost for x which furnish me that section" comparable factor. First multiply out the brackets: (x+10)(2x-3)=fifty 4 2x^2 + 17x - 30 = fifty 4 Then assemble to time-honored quadratic style: 2x^2 + 17x - 80 4 = 0 resolve via factorising (or via quadratic formula): (2x -7)(x+12) = 0 x = 7/2 or x= -12 -12 is incomprehensible if we are talking a pair of length to furnish an area, so x=7/2 = 3.5 is the only answer. (x+10)(2x-3) = (13.5)(4) = fifty 4 QED

Answer 5

Start with this.

lim x-->0 (cos 2x) = 1
lim x-->0 (sin 2x) = 0

Then we have:

lim x-->0 (cot 2x / sin 2x) =
lim x-->0 (cos 2x / sin^2 2x) = +∞
if approached from the positive side and

lim x-->0 (cos 2x / sin^2 2x) = -∞
if approached from the negative side

Answer 6

lim x->0 cot 2x/sin 2x

Since cot θ = cos θ/sin θ,
= lim x->0 (cos 2x/sin 2x)/sin 2x

Simplify the fraction
= lim x->0 cos 2x/sin² 2x

Use the identity cos 2θ = cos² θ - sin² θ
= lim x->0 (cos² x - sin² x)/sin² 2x

Use the identity sin 2θ = 2 sin θ cos θ
= lim x->0 (cos² x - sin² x)/(2 sin x cos x)²

Simplify the denominator
= lim x->0 (cos² x - sin²x)/4sin² x cos² x

Distribute the denominator
= lim x->0 (1/4sin² x - 1/4cos² x)

Distribute the limit
= lim x->0 1/4sin² x - lim x->0 1/4cos² x

Remove the constant, and use the reciprocal identities
= 1/4 lim x->0 csc² x - 1/4 lim x->0 sec² x

Therefore, since the limit of csc x as x approaches zero does not exist, it follows that
limit = does not exist

^_^

Answer 7

Yes, cot(2x)=cos(2x)/sin(2x); thus y = cot(2x)/sin(2x) = cos(2x)/(sin(2x))^2, while cos(0)=1 and sin(0)=0, then lim y = +infinity; this is the true answer! and dont challenge!

Answer 8

sad to say, i cant help. wen i was schooling 3 yrs back i was one of d top calculus students.

nw a friend in dire need is askn me about integration. check my last question to see if u can help

Answer 9

Northstar nailed it.

good job.

Answer 10

no idea, taking a shot in the dark here-------0