Question

Lim 1 / (tan5x*sinx) , х--0

Answer 1

Ответ:

Lim(х=>0) 1 / (tan5x*sinx) =1 / (tan(5*0)*sin0) =1 / (0*0) =1/0=∞

Answer 2

To find the limit of the expression as x approaches 0:

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lim (x -> 0) 1 / (tan(5x) * sin(x))

We can use the fact that tan(x) approaches x as x approaches 0 and that sin(x) approaches x as x approaches 0. Therefore, we can rewrite the expression as:

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lim (x -> 0) 1 / (5x * x)

Simplifying further:

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lim (x -> 0) 1 / (5x^2)

As x approaches 0, the denominator 5x^2 approaches 0, and the expression becomes undefined since you can't divide by 0.

Therefore, the limit does not exist in this case.