Exam 6: Inverse Functions

Use transformations to sketch the graph of the function.

Find the limit.

Use logarithmic differentiation to find the derivative of the function. y = (x + 7)^5/x

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.2x - 1.8x - 3.8; g(x) = -0.1x + 0.8x + 6.7

Differentiate the function.

Evaluate the given integral.

Suppose g is the inverse function of a differentiable function f and . If

Find the derivative of y.

Find, correct to three decimal places the area of the region above the hyperbola , below the x axis, and between the lines x = - 4 and x = - 3.

Differentiate the function. g(x) =

A painting in an art gallery has height h and is hung so that lower edge is a distance d above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle subtended at his eye by the painting?)

Find the derivative of the function. f (x) = 6 tan^-1 x²

Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches ft.

Find

Find

Find

Evaluate the limit using l'Hôpital's Rule.

Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass remaining after 38 days.

Find the values of for which satisfies the equation

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters. Find the slope of this curve where it meets the right pole.