Do you know if you have the right answer?

[Helical]

Hello, I'm going to begin undergraduate study next year (majoring in physics) and I have not taken any calculus yet. What I'm wondering is, with calculus can you check that your answer is right? Like with algebraic problems you can plug a variable back into your original equation and see if it comes out equivialent. This is just something I'm curious about and probably is a stupid question which stems from my ignorance of calculus. Anyways, thanks for any responses.

 

[enricfemi]

in fact, with calculus many questions can be checked. such as differential equation,you can check it like the way in algebraic equation.
but sometime, it's really hard to ensure ourself.

 

[Helical]

I see thanks for the response. The reason I'm curious is that I'm often not very confident so will recheck myself and like that ability with algebra. Good to know you can do it at least with some calculus.

 

[nicksauce]

In elementary calculus, if you are trying to evaluate the derivative of a function f(x) at a point x0, you can generally check your answer (with your calculator) against (f(x + epsilon) - f(x)) / (x + epsilon), for some small epsilon, like 0.0001.

When taking an integral you can simply check your answer by differentiating the anti-derivative you got.

And as already mentioned you can check your answers for differential equations by plugging in the answer you get and seeing if it indeed solves the equation.

 

[redrzewski]

There are also programs like Mathematica/Maple (and others) that'll let you verify most of your elementary calc answers.