Questions from General Calculus

Q: Differentiate the function. f (x) = sin (

Differentiate the function. f (x) = sin (ln x)

Q: The table shows the population of Nepal (in millions) as

The table shows the population of Nepal (in millions) as of June 30 of the given year. Use a linear approximation to estimate the population at midyear in 1989. Use another linear approximation to pre...

Q: Find the linearization L (x) of the function at a

Find the linearization L (x) of the function at a. f (x) = x4 + 3x2, a = -1

Q: Find the linearization L (x) of the function at a

Find the linearization L (x) of the function at a. f (x) = ln x a = 1

Q: Find the linearization L (x) of the function at a

Find the linearization L (x) of the function at a. f (x) = cos x, a = π/2

Q: Find the linearization L (x) of the function at a

Find the linearization L (x) of the function at a. f (x) = x3/4, a = 16

Q: Find the linear approximation of the function f (x) =

Find the linear approximation of the function f (x) = √1 - x at a = 0 and use it to approximate the numbers √0.9 and √0.99. Illustrate by graphing f and the tangent line.

Q: Draw a diagram showing two perpendicular lines that intersect on the y

Draw a diagram showing two perpendicular lines that intersect on the y-axis and are both tangent to the parabola y = x2. Where do these lines intersect?

Q: Find the linear approximation of the function g (x) =

Find the linear approximation of the function g (x) = 3√1 + x at a = 0 and use it to approximate the numbers 3√0.95 and 3√1.1. Illustrate by graphing g and the tangent line.

Q: Verify the given linear approximation at a = 0. Then determine

Verify the given linear approximation at a = 0. Then determine the values of for which the linear approximation is accurate to within 0.1.