Calculus Answers

Consider the function below. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)
f(x) = sqrt(x^2+3) - x

(a) Find the horizontal asymptote.
y = _____________

(b) Find the interval where the function is decreasing.
( _________, ____________)

(c) Find the interval where the function is concave up.
( _________, __________)

Consider the function f(x) = 5x[sup]7[/sup] + 2x - 1 amd the associated equation f(x) = 0.
a) show (by hand) that there is a unique simple root r in the interval [0,1].
b) use bisection procedure (maple) to approximate r to eight corrent decimal places. Report the approximation xc, the number of steps needed and the backward error |f(xc)|
c) use the newton's method (maple) to approximate r to right corrent decimal places (starting with xo = 0). Report the approximation xc, number of steps needed and the backward error |f(xc)|.

How can I use the concept in differentials to approximate a certain number which is not a perfect square?

Find the derivative. Simplify if possible.
f(t) = (sech(9e power t))2

Suppose k '(1) = 2.
(a) If f(x) = k(5x), find f '(1/5).
(b) If g(x) = k(x+ 2), find g '(-1).
(c) If h(x) = k(x / 7), find h '(7).

Find dy/dx by implicit differentiation.
9sin(x) + cos(y) = sin(x) cos(y)

Find the derivative of the function. Simplify if possible.

F(x) = arcsin ( square root of sin (11x))

Are
f(x)=x tan[sup]-1[/sup]x& & & & & & & & (- infinity,infinty);
f(x)=x^2 tan[sup]-1[/sup]x & & & [0, infinity) ;
f(x)= cos(lnx)& & & & & & & (0,1)
couniformly continuous on the given intervals ?

Differentiate the function.
y= (ln(1+e^x))^3