# Question and Answers Forum

LimitsQuestion and Answers: Page 1

lim_(n→∞) (1/n)((a+(1/n))^2 +(a+(2/n))^2 +...+(a+((n−1)/n))^2 )
lim_(x→2) ((((x^2 +4))^(1/3) −(√(x^3 −4)))/( (√(x^2 −4))−((x−2))^(1/3) ))
lim_(x→∞) (((x+a)^(1/x) −x^(1/x) )/((x+b)^(1/x) −x^(1/x) )) =?
find lim_(n→+∞) ∫_0 ^n e^(nx) arctan((x/n))dx
lim_(n→∞) (√(cosn+sinn−3^n +4^n ))
let f:[0,∞)→R be a continuous function if lim_(n→∞ ) ∫_0 ^1 f(x+n)dx = 2 then lim_(n→∞) f(nx) = ?
lim_(x→0) ((−x^3 +x)/(sin x))
lim_(x→0^+ ) xln(e^x −1)
−−−−−−− Ω = Σ_(n=0) ^∞ (( (−1)^( n) )/((−1)^( n) −n)) = ? −−−−−−−
calculate lim_(x→0) ((e^x −cosx)/x^2 )
lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?
lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?
A=lim_(x→0) ((sinx)/x^3 )=?
lim_(x→0) ((tan(tanx))/(sin(1−cosx)))
lim_(n→∞) ((⌊a⌋+⌊2a⌋+...+⌊na⌋)/n^2 ) where a∈R and ⌊x⌋ is the floor of x ∈ R
lim_(n→∞) n^(−n^2 ) [(n+1)(n+(1/2))(n+(1/2^2 ))...(n+(1/2^(n−1) ))]^n =?
Solve: lim_((x,y)→(0,0)) ((1−cos((√(10xy))))/(3.y.sin(22x))) Ans.: (5/(66)) Step by step, please!