Need help with these 1st year calculus problems, please help

[johnq2k7]

Please help me with these following problems:

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)

 

[Deleted member 4993]

Please help me with these following problems:

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)

Please show us your work, indicating where you are stuck - so that we know where to begin to help you.

 

[johnq2k7]

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

 

[Deleted member 4993]

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

You know that the range of the original function becomes the domain of the inverted function and the domain of the original function becomes the range of the inverted function.

So what is the range of y = sech(x)?