Questions from General Calculus

Q: Write the composite function in the form f (g (x

Write the composite function in the form f (g (x)). [Identify the inner function u = g (x) and the outer function y = f (u).] Then find the derivative dy/dx. y = e√x

Q: Find the x-coordinates of all points on the curve y

Find the x-coordinates of all points on the curve y = sin 2x – 2 sin x at which the tangent line is horizontal.

Q: A table of values for f, g, f', and

A table of values for f, g, f', and g' is given. (a). If h (x) = f (g (x)), find h'(1). (b). If H (x) = g (f (x)), find H'(1).

Q: Let f and be the functions in Exercise 53.

Let f and be the functions in Exercise 53. Exercise 53: A table of values for f, g, f', and g' is given. (a). If F (x) = f (f (x)), find F'(2). (b). If G (x) = g (g (x)), find G'(3).

Q: Find R'(0), R(x) = x +

Find R'(0), R(x) = x + 3x3 + 5x5/1 + 3x3 + 6x6 + 9x9 where Hint: Instead of finding R’(x) first, let f (x) be the numerator and g (x) the denominator of R (x) and compute R' (0) from f (0), f' (0), g...

Q: Write the composite function in the form f (g (x

Write the composite function in the form f (g (x)). [Identify the inner function u = g (x) and the outer function y = f (u).] Then find the derivative dy/dx. y = √2 - ex

Q: Find the derivative of the function. F (x)

Find the derivative of the function. F (x) = (x4 + 3x2 – 2)5

Q: Find the derivative of the function. F (x)

Find the derivative of the function. F (x) = (4x - x2)100

Q: Fanciful shapes can be created by using the implicit plotting capabilities of

Fanciful shapes can be created by using the implicit plotting capabilities of computer algebra systems. (a). Graph the curve with equation At, how many points does this curve have horizontal tangents?...

Q: Find the derivative of the function. F (x)

Find the derivative of the function. F (x) = √1 - 2x