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johnq2k7

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1.)Indicate whether each of the following functions is invertible in the given interval. Explain

a.) sech x on [0,infinity)

b.) cos (ln x) on (O, e^pie]

c.) e^(x^2) on (-1,2]

2.) Evaluate the following limits, justifying your answers. If a limit does not exist explain why.

a.) lim (x--> inf.) (3x^3 +cos x)/(sin x- x^3)

b.) lim (x-->Pie(+)) (tan^-1 (1/(x-Pie)))/(Pie-x)

c.) lim (x--> 0(+)) (sqrt(x+sin x))(ln x)

d.) lim (x--> 1(-)) (cos^-1(x))/(1-x)

3.) give the equation of the line tangent to the curve at the given point.

a.) (y)(tan^-1 x)= x*y at (sqrt(3),0)

b.) ln y= x^2 +(2)*e^x at (0, e^2)

My attempt at a solution for a.)

1.) sech x on [0,infinity)

let y= sech x

therefore, y*sech^-1 x= sech^-1 x* sech x

therefore x= y*sech^-1 x

since it is an inverse function switch x and y variables

therefore f^-1(x)= x*sech^-1 (y)

how do i determine, it's intervible in [0, infinity)... I'm not sure if this prior work is correct