Calculus Answers

Show that for every real number x > 0, there exists a real number y > 0 such that |2x + y| = 5

Show that there is real number x so that |x−1| = |x−2|.

Prove that the set A given by A:={2020/n +n² : n∈N} is unbounded above.

Use induction to prove that 1³+2³+...+(n−1)³ < n⁴/4 < 1³+2³+...+n³

Express the following function, F(x), as a composition of two functions, f and g. f(g(x)).

F(x)= x^2/(x^2+4)

Verify that f(g(x)) = F(x)

The derivative of f is x^3(x+5)(x-1). At which values of x will the graph of f have a relative maximum? A relative minimum?

Let f be the function given by f(x)=-x^2/3. Which of the following statements about f are true?

I. f is continuous at x=0.

II. f is differentiable at x=0;

III. f has an absolute maximum at x=0

apply intermedaite value theorem on x^5-x^3+3x-5

Can the intermediate value theorem can be applied to show the that there is a root of equation x^5-x^3+3x-5 in the given interval [1,2] if yes, apply it

The graph of every function from [0,1] to R is infinite. True or False