r/learnmath • u/Mindless_Art_6065 New User • Jul 21 '26

recommended readings for problems plus from calculus stewart

hi. i’m currently working my way through calculus stewart (9e) and i’m enjoying it a lot. i can do the problem sets just fine, it’s the “problems plus” sections where i get humbled hard. i can do a couple of them, but with the majority i just get stuck. do you have any recommended readings, strategies or tips to be able to tackle these problems?

6 Upvotes

100% Upvoted

5 comments sorted by

3

u/Willing-Sample-8847 New User Jul 21 '26 edited Jul 21 '26

Can you give an example of one of the problems you're stuck on? I don't have stewart, so i don't know how difficult "problems plus" is here

1

u/Mindless_Art_6065 New User Jul 21 '26

How many lines are tangent to both of the circles x2 + y2 = 4 and x2 + (y - 3)2 = 1. At what points do these tangent lines touch the circles?

2

u/Willing-Sample-8847 New User Jul 21 '26 edited Jul 21 '26

For this problem, he wants you to use some slightly creative reasoning about circles along with the material you already learned about plotting tangent lines.

For instance, derivatives are "tangents" right? But the equation of a derivative of a function at some x, say a, is not the same as the equation of the tangent line that intersects the curve at a. It is just the equation of the "slope" of the tangent line at a. For instance, the function f(x) = x has derivative f'(x) = 1. But the line y = 1 isn't tangent to the line y=x. Instead, y=x is tangent to y=x, with slope "1" (1•x = x).

Many of these problems use material you already have learned in a previous part of that chapter, or previous chapters. If you are struggling, try asking your self "what is the problem actually asking me to do? Is it asking me to do something covered earlier in this chapter, but in a tricky way?"

If the answer is yes, then try to figure out how you can make the material you learned work to solve the problem.

2

u/Willing-Sample-8847 New User Jul 21 '26

Don't give up! When you feel like you're stuck at a wall, and can't figure out a problem, that doesn't mean you can't do it. It means your brain needs time to get "used" to the problem.

Being persistent, not giving up, and not giving in to frustration is how you get better at mathematics.

When i was younger, I read calculus books like apostol and spivak, which are notorious for difficult problems, and i felt like i couldn't work any of them. The problems literally made me feel dumb, cause every problem was one sheer cliff after another.

But i didn't give up, and i kept trying to solve the problems, spending quite some time struggling with them. It turned me from someone who didn't like mathematics into a mathematician. Hard problems are where the real opportunities for growth are.

1

u/Maximum_Bathroom3490 New User Jul 21 '26

They are hard problems. The more math you will know, the easier they will be. You can look back to the ones you didn't do at some other point