Calculus Answers

Evaluate the ∫y(y²-2)²dy

Evaluate the ∫√5xdx

Find arc length of curve (sketch also) x=y^4 /8 + 1/4 y^2 , y=1 to y = 4

Differentiate (3x+2)⁴

Show that ∞n=1[(−1)^(n−1)].[(x^n)/(n)] converges if |x| < 1

Show that ∞n=0 (x^n)/(n!)converges for all x ∈ R.

Show that ∞n=1 (x^n)/(n^n) converges for all x ∈ R

Prove that the series 1 + (1/2)·(1/3) + [(1·3)/(2· 4)]·(1/5) + [(1·3·5)/(2·4·6)]·(1/7) + ..... converges

Prove that the series ∞n=1 n^n/n! diverges

Let {an}∞n=1 be a convergent sequence. Prove that {an}∞n=1 satisfies Cauchy’s criterion