Calculus Answers

Evaluate the limit as x turns to 1^-

Lim [sin(x²-1) / e^(Inx) - 1]

Solve the inequality

x>√(x+2)

IxI / Ix+1I -1 > 1

Evaluate ∫₀^π √(1+cos8xdx)

Evaluate the limit as x turns to 2⁺

lim {sin[In (x-1)] / √(x-2)}

Calculate the volume created by revolution around the axes OX, of D of the plane (OXY) where D={(x,y) ∈R: 0 ≤ y ≤x, (x-2)² +y² ≤ 4}

Simplify the sum Σ from r=0 to 2n+1 of [3/(r+1)(r+2)]

Evaluate the limit as x turns to -∞

Lim [3x + √(9x²-Ix-2I)]

Consider the following integral:

I =  ∫ 1 / (√2x²-x²) dx

(a) complete the square of f(x) = 2x²-x²

(b) use (a) together with the method of trigonometric substitution to determine the integral.