Questions from General Calculus

Q: Find an equation of the tangent to the curve at the given

Find an equation of the tangent to the curve at the given point. x = t3 – 2t2 + t + 1, y = t2 + t, (1, 0)

Q: Find equations of the tangent line and normal line to the curve

Find equations of the tangent line and normal line to the curve at the given point. y = (2 + x) e-x, (0, 2)

Q: The total fertility rate at time t, denoted by F (

The total fertility rate at time t, denoted by F (t), is an estimate of the average number of children born to each woman (assuming that current birth rates remain constant). The graph of the total fe...

Q: (a). If f (x) = x√5

(a). If f (x) = x√5 - x, find f'(x). (b). Find equations of the tangent lines to the curve y = x√5 - x at the points (1, 2) and (4, 4). (c). Illustrate part (b) by graphing the curve and tangent lines...

Q: (a). If f (x) = 4x – tan

(a). If f (x) = 4x – tan x, -π/2 < x < π/2, find f' and f". (b). Check to see that your answers to part (a) are reasonable by comparing the graphs of f, f', and f".

Q: A car starts from rest and its distance traveled is recorded in

A car starts from rest and its distance traveled is recorded in the table in 2-second intervals. (a). Estimate the speed after 6 seconds. (b). Estimate the coordinates of the inflection point of the...

Q: Recall that a function f is called even if f (-x

Recall that a function f is called even if f (-x) = f (x) for all x in its domain and odd if f (-x) = -f (x) for all such x. Prove each of the following. (a). The derivative of an even function is an...

Q: The graph of a function is shown. Sketch the graph of

The graph of a function is shown. Sketch the graph of an antiderivative F, given that F (0) = 0.

Q: (a). Find an equation of the tangent to the curve

(a). Find an equation of the tangent to the curve y = ex that is parallel to the line x – 4y = 1. (b). Find an equation of the tangent to the curve y = ex that passes through the origin.

Q: Find a parabola y = ax2 + bx + c that passes

Find a parabola y = ax2 + bx + c that passes through the point (1, 4) and whose tangent lines at x = -1 and x = 5 have slopes 6 and -2, respectively.