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 Apr 10 answered Finding a parameter of a function Apr 10 comment Finding a parameter of a function Does the question say whether there is only one value of $a$, or are you supposed to determine how many there are and find them? Apr 10 comment Finding a parameter of a function You could in principle use the cubic formula. Apr 10 comment Let $E \subset ℝ^n$ open and $f:E→ℝ^m$. Then is $f$ cont. diffb. on $E$ $⇔$ all the partial derivatives $D_jf_i$ exists on $E$ and are cont. on $E$. @PeterTamaroff: Oh, that makes sense. Apr 10 comment Let $E \subset ℝ^n$ open and $f:E→ℝ^m$. Then is $f$ cont. diffb. on $E$ $⇔$ all the partial derivatives $D_jf_i$ exists on $E$ and are cont. on $E$. Wait, isn't this the definition of continuously differentiable? Apr 10 comment Prove that $f$ is continuous, $f'$ is bounded… I'm guessing your $x = 0$ and $x \neq 0$ conditions are mixed up. Apr 10 comment For which numbers $c$ is there a number $x$ such that $f(cx)=f(x)$? Which exercise is this? I think there's something I'm not understanding. Apr 10 comment For which numbers $c$ is there a number $x$ such that $f(cx)=f(x)$? What's $f$ here? Apr 10 comment Why translation of vectors doesn't preserve the cosinus of the angle they form? How can you add a scalar to a vector? Apr 9 comment Gradient of scalar potential By the square of a vector, do you mean the square of its length? Apr 9 revised Mathematical Induction: how do we know what applies to one thing also applies to another? added 1857 characters in body Apr 9 comment Mathematical Induction: how do we know what applies to one thing also applies to another? @Hal: We don't have two examples. $P(2)$ fails, because $p_{2+1} - p_2 = p_3 - p_2 = 5- 3 = 2 \ne 1$. The good thing about induction is that we don't have to check all the natural numbers, because we can't: There are infinitely many of them! We don't prove a statement by checking enough special cases. Give me a while and I'll add a bit of clarification to my answer. Apr 9 comment Solution of $ax=a^x$ In general, you can't find a simple expression for the solution. Apr 9 answered Mathematical Induction: how do we know what applies to one thing also applies to another? Apr 8 comment Nonzero derivative implies function is strictly increasing or decreasing on some interval I'm trying to prove this without assuming the derivative is continuous, but first I gotta ask: is it actually true? Apr 7 comment Nonzero derivative implies function is strictly increasing or decreasing on some interval Wouldn't the fact that derivatives satisfy the intermediate value property suffice? Apr 7 comment Jacobian of the change of variables Maybe it would help to show what you did and what you got. Apr 7 comment Calculus inverse function solving for $f^{-1}$ @user71317: $f$ is either always positive or always negative. $f(1) = 2$ says that it's always positive. Apr 7 comment Interval of definition of the solutions of $\dot x=e^x\sin x$ Isn't every continuous function locally Lipschitz? Apr 6 answered Help with $\arcsin(x)$ derivative and differentials.