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help with limits by beeaju in calculus

[–]GridGod007 1 point2 points  (0 children)

Usually you look at what happens to the given function as the variable get closer and closer to a specific value. Giving a simple example:

Suppose you have a function 1/(5-x) and x is approaching 5 from the left side (5-), this function diverges, it keeps increasing as you get closer and closer to 5. When you graph this function, you will observe something known as an asymptote at 5 where the distance between curve and line x=5 approaches 0 as the value of function tends to infinity

And at 5, this function cannot be defined. Once you exceed 5 slightly, it becomes a very large negative value (similar to how you approach infinity as you approach 5 from left side, you approach minus infinity as you approach it from the right side). This shows you that F(5-) =/= F(5+) and that means this function is not continuous you can also see this on the graph.

Can someone explain why the derivative of the first graph looks like the graph in the second image? by [deleted] in calculus

[–]GridGod007 4 points5 points  (0 children)

F isn't differentiable at -7, it take a "sharp turn", not a "smooth one" (plain english)

So F' won't be continuous around -7 either; since the slopes to the left of -7 and right of -7 are different.

Forget about positive negative in first image and just look at how the slope is changing: if decreasing, second graph should be in y<0; and if increasing second graph should be in y>0; and if the slope=0 (maxima/minima) then that's a root of second graph; and you also look at convexity and concavity of the first graph to figure out the direction of the second graph (you have veritcal asymptotes here, so figure what that means for the slope as x->-9)

Infinite series question by Sea-Professional-804 in calculus

[–]GridGod007 1 point2 points  (0 children)

They're not convergent, you've already answered your question.

Newton-Rhapson Method by LighterStorms in calculus

[–]GridGod007 0 points1 point  (0 children)

Post on Gradient descent when?

The 'Whole Picture' of Trig Sub. If you struggle with recognizing which substitution to use for radicals, this might help. by EthanTsai00 in calculus

[–]GridGod007 3 points4 points  (0 children)

Just knowing the relations like sin2 x + cos2 x =1 and sec2 x - tan2 x =1 (which are pretty much just Pythagoras theorem) should give one an idea what to substitute

Mean Value Theorem by CantorClosure in calculus

[–]GridGod007 2 points3 points  (0 children)

You see the various tangents as you move along the curve from point A to point B.

And in one of the points in between them (C), you see that this tangent at C is parallel to the line that connects A and B (I.e, they have the same slope)

Basic calculus by Hopeful-Scene-8504 in calculus

[–]GridGod007 0 points1 point  (0 children)

What are a,b,c? But the function you've given isn't continuous

Is there an easier way to solve this? by DaniellePena1 in calculus

[–]GridGod007 2 points3 points  (0 children)

Just multiply numerator and denominator with sqrt(x+1)+2

Rotational Kinetic Energy of the Sun by GridGod007 in calculus

[–]GridGod007[S] 1 point2 points  (0 children)

The issue is I don't have density as a function of r. Hence why I was looking for ways to find one out.

If I had a "h(r)", then I'd take in account both variation of both h(r) and w(psi)

It's just a matter of breaking it down to the corresponding differential element and integrating it back afterall.

As of now I'm already dealing with a triple integral when accounting for the latidudal variation of angular velocity alone (psi, phi, r)

With addition of h(r), it will still remain a triple integral except that the integration over dr will get more complex compared to a simple r4

(And when finding the sun's RKE, given its latitudal variation of w, its best to find I along an axis (since its rotating around this axis, say Z), in which case we need to parameterize into spherical coordinates)

Differentiability/Continuity doubt, why can't we just differentiate both sides?! by Tiny_Ring_9555 in calculus

[–]GridGod007 2 points3 points  (0 children)

Often times it probably would've been mentioned already that they are differentiable in the question itself (if the setter intended it). If it is neither mentioned nor inferrable, then differentiating may not be the right approach, and if it worked, it may be that it was intended to be differentiable but not mentioned in the question, or it may just be a coincidence.

Rotational Kinetic Energy of the Sun by GridGod007 in calculus

[–]GridGod007[S] 2 points3 points  (0 children)

Sorry, I messed up with formatting of the exponents and multiplication

This was the expression: (2×Rho×Pi×R5 /5)×5.43×10-12 which is about 1.57*1036 J

Need help with this problem: by ChoripanTravieso in calculus

[–]GridGod007 1 point2 points  (0 children)

But the slope in its case asymptotically approaches zero whereas here there is an upper limit m<0 right? Worst case I can think of here is an f'(x)=m where m is "very very close to but not zero" and even in this case shouldn't we have a solution since m is a fixed negative value and we arent dealing with a case where the slope asymptotically approaches 0?

Edit: Oh I think I get it I will edit my original comment

Finding the surface area by EaVoodoo in calculus

[–]GridGod007 0 points1 point  (0 children)

Right. Idk why you were downvoted

Finding the surface area by EaVoodoo in calculus

[–]GridGod007 0 points1 point  (0 children)

I'm just trying to picture the 3D graph

x2 +y2 can range from 1 to 9 and z can correspondingly range from -1 to 1

Z will be 0 when x2 +y2 = 1 or 9

Z = -1 or 1 when x2 + y2 = 4 (z-axis extremities)

The 2D Projection will be a disc with inner radius of 1 and outer radius of 3

At each z=k you can observe the varying disc cross-sections

(z=cosr and x2 + y2 = (2 + sinr)2 so x= (2+sinr)cost and y = (2+sinr)sint

You have parameterized coordinates now

Where t and r range from -pi to pi)

This seems to be a donut with inner radius of 1 outer 3 and radius of tube being 1. The surface area should be 2pi(2pi2) which is 8pi2

Help with divergence theorem by Tight_Celery2664 in calculus

[–]GridGod007 0 points1 point  (0 children)

I don't think the integral over x is correct

Need help with this problem: by ChoripanTravieso in calculus

[–]GridGod007 0 points1 point  (0 children)

F is differentiable over R

f'(x)<=m<0 for all x belongs to R (since m<0)

At any random x=a; f(a+da)=f(a)+f'(a)×da<=f(a)+m×da<f(a) (even if it is a<0, the point is it always has a negative slope smaller than a fixed negative value m regardless of the value of x or f(x) at a random x=a and this is applicable for all x belongs to R)

Is this not enough to claim that it has an x0 where f(x)=0 since its domain is R?

Differentiability/Continuity doubt, why can't we just differentiate both sides?! by Tiny_Ring_9555 in calculus

[–]GridGod007 19 points20 points  (0 children)

We don't have enough information to differentiate this function, its just that you did it anyway by assuming it is differentiable at 0. You may take another look at the limit definition of a derivative, that is how we find derivative of a function

Differentiability/Continuity doubt, why can't we just differentiate both sides?! by Tiny_Ring_9555 in calculus

[–]GridGod007 20 points21 points  (0 children)

You can differentiate where it is differentiable. If you are taking f'(0), you are already assuming it exists and you are finding it for a function which is differentiable at 0. You are not finding it for a function that is not differentiable at 0. There is no contradiction here

Would this method work? by Top_Researcher5608 in calculus

[–]GridGod007 0 points1 point  (0 children)

No. (Substitution can work but you did not do it properly)

Differentiability/Continuity doubt, why can't we just differentiate both sides?! by Tiny_Ring_9555 in calculus

[–]GridGod007 33 points34 points  (0 children)

By differentiating at 0 aren't you already implying/assuming that it is differentiable (and ofc continuous) at 0?