Recent content by Kazane

Homework Statement Determine equations of all lines the are tangent to y=x^2/(x-1) and that pass through the point (2,0). Homework Equations The Attempt at a Solution First I found the y' which I came up with y'=x(x-2)/(x-1)^2 next, let (a,f(a)) and put a to y'...

Homework Statement f(x)=x1/3 use the definition of f'(a) to calculate the slope of the curve at x=1 (Hint: by rationalizing the numerator. useful formula a3 -b3=(a-b)(a2+ab+b2) The Attempt at a Solution f'(x)=lim (x->1) f(x)-f(1)/x-1 =lim (x->1) x1/3-11/3/ x-1 How can I do x1/3-11/3...

Homework Statement The graph of f goes through the origin; f is increasing at an increasing rate on the interval (0,1) and at a decreasing rate on (6, Infinity); f is constant on the interval (2,4); f is decreasing at an increasing rate for all other positive values of x; f(1)=2, f(3)=1...

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Homework Statement Show how to determine the domain of each of the following functions: a) f(x) = ln(1 - ln(x)) b) g(x)=(x^2 -1)/(x^4・e^2x - 2x^2・e^2x - 8e^2x) c) h(x)= sqrt(6-e^-5t) Can somebody show me how to do these questions? Homework Equations The Attempt at a Solution I...