Calculus Answers

Use the definition of limit to prove that the sequence { 1/√n+1 } converges to 0

Use the definition of limit to prove that the sequence {n-1/n} n=1 to infinity is divergent

Let l be any positive integer. Use sandwich theorem for sequences to prove that the sequence {1/n^ l} converges to zero.

If a=(xz^(3))i-(2x^(2)yz)j+(2yz^(4))k find curl a at (1 -1 1)

Determine the limit when x goes to 0 of (sin(1/x)) if it exists.

For a particular predator-prey relationship, it was determined that the number y of prey consumed by an individual predator over a period of time was a function of the prey density x (the number of prey per unit area). Suppose that y=f(x)=(10x)/(1+0.1x)

If the prey density were to increase without bound, what value would y approach?

Determine the limit when x goes to infinity sqrt(x^(2)+x)-x if it exists.

Let {an}∞n=1 be a sequence converges to a limit L ∈ R. Prove that any subsequence of {an}∞n=1 is convergent and converges to the same limit L.

Let {an}∞n=1 be a bounded sequence and {bn}∞n=1 be a sequence converges to 0. Prove that the sequence {an · bn}∞n=1 converges to 0.

Determine the limit when x goes to zero (x^(2)+5x-4)/(x^(2)+1) if it exists.