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Added missing note for dis hw3
1 files changed, 1 insertions, 1 deletions
| -rw-r--r-- | Year 1/Calculus/Homeworks/Homework3.tex | 2 |
diff --git a/Year 1/Calculus/Homeworks/Homework3.tex b/Year 1/Calculus/Homeworks/Homework3.tex index 60460f0..bc979a1 100644 --- a/Year 1/Calculus/Homeworks/Homework3.tex +++ b/Year 1/Calculus/Homeworks/Homework3.tex @@ -57,7 +57,7 @@ \paragraph{Решение:} Развиваме функциите в дробта по Маклорен: \begin{align*} & \ln (x^2 + 1) = x^2 + o(x^2) \qquad e^x = 1 + x + \frac{x^2}{2} + o(x^2) \qquad \cos x = 1 - \frac{x^2}{2} + o(x^2) \\ - & (1 + 12x)^{\frac{1}{4}} = 1 + \frac{1}{4}12x + \binom{\frac{1}{4}}{2}x^2 + o(x^2) = 1 + 3x - \frac{27}{2}x^2 + o(x^2) \\ + & (1 + 12x)^{\frac{1}{4}} = 1 + \frac{1}{4}12x + \binom{\frac{1}{4}}{2}\colorbox{Dandelion}{144} x^2 + o(x^2) = 1 + 3x - \frac{27}{2}x^2 + o(x^2) \\ & \quad (\tg (x^2))' = \frac{(\sin (x^2))' \cos (x^2) - \sin (x^2) (\cos (x^2))'}{\cos^2 (x^2)} = \frac{2x \cos^2(x^2) + 2x \sin^2(x^2)}{\cos ^2 (x^2)} = \frac{2x}{\cos ^2 (x^2)} \\ & \quad (\tg (x^2))'' = \left( \frac{2x}{\cos ^2 (x^2)} \right)' = \frac{(2x)'\cos^2 (x^2) - 2x(\cos^2 (x^2))'}{\cos^4(x^2)} = \frac{2\cos^2 (x^2) + 8x^2\sin (x^2) \cos(x^2)}{\cos^4(x^2)} \\ & \quad \tg(0) = 0, \quad (\tg(x^2))'(0) = 0, \quad (\tg(x^2))''(0) = \frac{2}{2} x^2 \implies \tg (x^2) = x^2 + o(x^2) |