Aayush Agrawal
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 Mar 29 comment Why is the tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ given by $y = mx + \sqrt{a^2m^2 + b^2}$ @TheodorosMpalis The slope Mar 29 asked Why is the tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ given by $y = mx + \sqrt{a^2m^2 + b^2}$ Mar 15 comment Where did i go wrong in trying to find the intervals where y is increasing and decreasing? @TheOddbodNumber I just learned about it so was practicing it. Mar 15 accepted Where did i go wrong in trying to find the intervals where y is increasing and decreasing? Mar 15 comment Where did i go wrong in trying to find the intervals where y is increasing and decreasing? There is a tiny typo, i think you confused $x +1$ with $x + 2$. Also while i do understand that, that makes me even more confused, since then 2x - 2 is the determiner of slope sign, which would give only a single interval, even though the other method gives four intervals. Mar 15 asked Where did i go wrong in trying to find the intervals where y is increasing and decreasing? Mar 15 accepted How do you check which intervals a cubic function will increase and in which intervals it will decrease? Mar 15 comment How do you check which intervals a cubic function will increase and in which intervals it will decrease? @Mufasa I already differentiated it, that's how i got that the differential is zero at {-2,3}. What i don't know is which of the three intervals i get would the function be strictly increasing or strictly decreasing in. Mar 15 revised How do you check which intervals a cubic function will increase and in which intervals it will decrease? added 20 characters in body Mar 15 asked How do you check which intervals a cubic function will increase and in which intervals it will decrease? Mar 15 accepted Why is the graph of a quadratic function a parabola? Mar 15 accepted For the differentiation of $x^{\frac23} + y^{\frac23} = a^{\frac23}$, why is the substitution $x = a \cos^3\theta$ legal? Mar 15 accepted Prove that if $x = \sqrt{a^{\sin^{-1} t}}$ and $y = \sqrt{a^{\cos^{-1}t}}$ then $\frac{dy}{dx}$ = $-\frac{y}x$ Mar 15 asked Prove that if $x = \sqrt{a^{\sin^{-1} t}}$ and $y = \sqrt{a^{\cos^{-1}t}}$ then $\frac{dy}{dx}$ = $-\frac{y}x$ Mar 14 comment For the differentiation of $x^{\frac23} + y^{\frac23} = a^{\frac23}$, why is the substitution $x = a \cos^3\theta$ legal? I think i get the idea, but that's still just an example. Can you provide a more rigid proof that x and y must lie between a and -a? Mar 14 comment For the differentiation of $x^{\frac23} + y^{\frac23} = a^{\frac23}$, why is the substitution $x = a \cos^3\theta$ legal? @dbanet Unfortunately that's all there is to it. The exact words of the excercise are "Find $\frac{dy}{dx}$, if $x^{\frac23} + y^{\frac23} = a^{\frac23}$". The exercise itself is from a local school textbook. Mar 14 asked For the differentiation of $x^{\frac23} + y^{\frac23} = a^{\frac23}$, why is the substitution $x = a \cos^3\theta$ legal? Mar 6 comment Why is the graph of a quadratic function a parabola? Yes, but doesn't simple plotting not necessarily prove that the curve is a parabola? Unlike a square or a rectangle, we can only say that the curve looks like a parabola. Mar 5 awarded Custodian Mar 5 reviewed No Action Needed Formula for a geometric series weighted by binomial coefficients (sum over the upper index):$\sum_{i=0}^L {n+i\choose n}\ x^i =\ ?$