Найти пределы УРАВНЕНИЯ lim x→3
x2−9 x2−2x−3
lim x→π 4
sinx−cosx cos2x

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вопрос

Factorizing the numerator and denominator gives:

lim x→3 (x - 3)(x + 3) / (x - 3)(x + 1)

Now we can cancel out the common factor (x - 3) from the numerator and denominator:

lim x→3 (x + 3) / (x + 1)

Plugging in x = 3 gives:

(3 + 3) / (3 + 1) = 6 / 4 = 3/2

Therefore, the limit of the expression as x approaches 3 is 3/2.

Applying the trigonometric identity cos(2x) = cos^2(x) - sin^2(x) gives:

lim x→π 4 (sinx - cosx) / (cos^2(x) - sin^2(x))

Now, substituting the values for sinx and cosx at x = π gives:

(0 - (-1)) / (1 - 0) = 1 / 1 = 1

Therefore, the limit of the expression as x approaches π is 1.