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Bookmark or Share- Why the limit of $\\frac{\\sin(x)}{x}$ as $x$ approaches 0 is 1?$\begingroup$ You can't calculate exact value of sin(x)/x for x=$0$. When you say x tends to $0$, you're already taking an approximation.So, we have to calculate the limit here.Taylor series gives very accurate approximation of sin(x), so it can be used to calculate limit. $\endgroup$ –
- calculus - Finding $\int x^xdx$ - Mathematics Stack ExchangeStack 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.
- Proof of the derivative of $x^n$ - Mathematics Stack ExchangeAnother proof of. (xn) ′ = nxn − 1, ∀n ∈ N. can be implemented with induction on n using the product rule. (f ⋅ g) ′ = f ′ g + fg ′. and the trivial identity derivative. (x) ′ = 1. Specifically: For n = 0, (x0) ′ = (1) ′ = 0 = 0 ⋅ x − 1 holds. For n = 1, (x1) ′ = 1 = 1 ⋅ x0 holds.
- functions - What does 'express in terms of $x$' mean? - Mathematics ...Idiomatically speaking, to write a function “in terms of” a given variable or variables means to write an algebraic expression using only that variable or variables. So for instance, given an equation x + 2y − 3z = 0 x + 2 y − 3 z = 0, we can solve for z z in terms of x x and y y as z = 1 3(x + 2y) z = 1 3 (x + 2 y).
- $X$ is Hausdorff if and only if the diagonal of $X\\times X$ is closedLet $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$ Show that $X$ is Hausdorff if and only if $D ...
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