Calculus/Expert Profile

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Recent Answers from Socrates

2012-01-19 Calculus:

This is not really a calculus problem. Observe that -4√(2-x) is always less than or equal to zero because √(2-x) is always greater than or equal to 0  . So 0 , which occurs when x=2 , must

2011-12-02 Rate of Change of The Volume of A Cone:

Let E(a) be the rate of evaporation when the surface area of the circular region on top is a.  We are told that the rate of evaporation is directly proportional to the area. This means that E(a)=ca , for

2011-11-28 Calculus, Find Integral:

You want to find     S |x|x^2 dx from -1 to 1      and    S |x|[sin(x)]^3 / [1+cos(x)] dx from -1 to 1    then add these two values      For the first integral ,       S |x|x^2 dx from -1 to 1 = S |x|x^2

2011-11-24 Integral Question:

S f(x) dx from 0 to 4 is 10. Make the change of variables x=2y , then dx/dy = 2 and dx = 2 dy . Since y = (1/2)x , the new limits for the integral in the variable y become 0 to 2.    We now have 10 = S

2011-05-19 limits:

Evaluate the natural log of this limit , then raise e to your answer.    ln[(x^2+5x+6)/(x^2+2x+3)]^x  = xln[(x^2+5x+6)/(x^2+2x+3)]  =    ln[(x^2+5x+6)/(x^2+2x+3)]/ x^-1    use L'Hospital's Rule and simplify