Recent content by JessicaJ283782

When would you use trig substitution vs. partial fractions? I know partial fractions is when you have a polynomial over a polynomial, but some of the problems in the trig substitution section in my book had polynomial over polynomial and used trig substitution?

I've always kind of wondered this, but professors like when students stop by their office hours the first or second week of class to introduce themselves?

Homework Statement Differentiate using implicit differentiation y^2sin(x) Homework Equations I know you need the chain rule and the product rule to solve this The Attempt at a Solution So, it would be: 2yy' + y^2cos(x) Is that correct?

Do you have any hints on how to pick which one by any chance? Or how you can look at them and tell which one to "break up"?

trigonometric integrals; choosing which one to "break up?" When you have two different trigonometric functions multiplied together within the integral, for example integral of (cos^4*sin^6) how do you tell which one to "break them up" to substitute an identity in? Thank you!

If I honestly really like the University I am currently at, so I was wondering if it is acceptable to get all three degrees in Mathematics from this institution if I want to become a Math professor? Some of the professors in their department got all of their degrees from the same university, but...

Homework Statement It is given that integral(1 to 2) g(x)dx=22 integral (1 to 4) g(x)dx=7 integral (1 to 16) g(x)dx=13 Find integral (4 to 16) Homework Equations Using properties of integrals, integral(4 to 16)= integral(1 to 16) - integral(1 to 4) The Attempt at a...

Thank you so much! I really appreciate it!

It would be (0, ∞) since the critical point is 0 because it makes the fraction zero. Concave up means f"(x)>0 and f"(x) is positive when the function is evaluated at any number greater than 0. If you evaluate the function at -1, for example, you would get a negative number, so it would be...

The numerator would give only a critical point of 0 since that is the only place it is not defined, right? So then it would be concave up on (0, infinity)?

I apologize for the typo! So it would be: x/√(1+x^2) The only critical number would be 0 then, so wouldn't it be concave up on (-infinity, 0) and (0, infinity) since the denominator is always positive because of the square root?

Homework Statement x Determine all intervals over which the function f(x)=∫√(1+t^2) dt is concave upward 1 Homework Equations I know concave...

Homework Statement Find the derivative of: x+xy=y^2 Homework Equations So I know you have to differentiate it, and it would be: 1+xyy'=2yy' The Attempt at a Solution Moving the terms with y' to one side: 1+xyy'-2yy'=0 xyy'-2yy'=-1 Factoring out y'...

Homework Statement Find the limit-> 2 g(x)= (x^2-3) if x < 2 3 if x=2 cos(x-2) if x>2Homework Equations So, I know you basically ignore the limit at 2, and you need to check it from the right and left. So, you want the x^2-3 and...

When do you use "u-substitution" in integration? I understand how to use it, but I'm just getting really confused on when you use it? Is there a way you can look at the problem and tell you need substitution vs. other methods? We have a final coming up, and obviously we won't have too much time...