Calculus Answers

∫x^2 sqrt(2-x)dx

Explain if the limit of the function f(t) exist at t=1 where,

F(t)={ t²+5 if t<1} 

 {3-3t if t>1}

Explain if the limit of the function f(t) as t approaches 0, where f(t)=ln(t)

Explain if the limit of the function f(t) exist at t=1 where,

F(t)={ +5 if t<1} 

  {3-3t if t>1}

Sec²(A/2)= 2-2 cos A/ sin² A

Cos(5x)cos(2x) + sin(5x)(sin(2x)

Suppose {an} ∞ n=1 be a sequence of positive real numbers and 0 < x < 1. If an+1 < x · an for every n ∈ N, prove that limn→∞ an = 0.

Prove that if a sequence {an}∞ n=1 satisfies Cauchy’s criterion, then it is bounded.

Let {an} ∞ n=1 and {bn} ∞ n=1 be sequences both of which diverge to −∞. Then {an + bn} ∞ n=1 diverge to −∞ and {an · bn} ∞ n=1 diverge to +∞.

Let {an}∞ n=1 and {bn}∞ n=1 be sequences both of which diverge to +∞. Then both of {an + bn}∞ n=1 and {an · bn}∞ n=1 diverge to +∞.