For the particular problem at hand, the method isn't as fast as the approach in the comments; but it's routine. $$\frac{dx}{\sqrt{C-x^2}}=\pm dt$$ $$\int{\frac{dx}{\sqrt{C-x^2}}}=\pm \int{dt}$$ $$\tan^{-1}\frac{x}{\sqrt{C-x^2}}=\pm t + K$$ $$\frac{x}{\sqrt{C-x^2}}=\tan{(\pm t + K)}\,.$$ Square both sides, rearrange, use the identity $1+\tan^2 ...

2017年1月22日 · 1) x^a × x^b = x^a+b; for x = 0 and a = 0, you would get 0^0 × 0^b = 0^b = 0, so we can't tell anything -- except confirm that 0^0 = 1 still works here! 2) x^{-a}=1/{x^a} -- so when a = 0 , x^{-0} = 1/x^0 = x^0 , which again does work for 0^0 = 1 ; 3) {x^a}^b = x^{a×b} , thus x^(1/n) is the n-th root -- and 1/n = 0 for no value of n , so ...

2017年6月21日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2015年11月2日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2016年3月3日 · #lim_{x rarr 0} x/{sin x} = lim_{x rarr 0} 1/{cos x} = 1/{cos 0} = 1/1 = 1#. NOTE The question was posted in " Determining Limits Algebraically " , so the use of L'Hôpital's rule is NOT a suitable method to solve the problem.

2016年11月20日 · $\begingroup$ The statement says that the conclusion follows if the inequality is true for all $\epsilon > 0$. $. Fixing $\epsilon$ at a particular value is not meaningful, especially if that value is possibly outside of the range of $\epsilon$ that you are allowed to consider. $\end

2016年6月30日 · There is no x such that e^x = 0 The function e^x considered as a function of Real numbers has domain (-oo, oo) and range (0, oo). So it can only take strictly positive values. When we consider e^x as a function of Complex numbers, then we find it has domain CC and range CC "\\" { 0 }. That is 0 is the only value that e^x cannot take. Note that e^(x+yi) = e^x …

2016年1月6日 · Using only the definition of Absolute Value: $\left|x\right| = \begin{cases} x & x> 0 \\ -x & x < 0 \\ 0 & x = 0,\end{cases}$ Prove that $|-x| = |x|.$ This ...

2020年6月3日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.