Questions from General Calculus

Q: Find f' (a). f (t) = 2t

Find f' (a). f (t) = 2t + 1/t + 3

Q: (a). Find the slope of the tangent line to the

(a). Find the slope of the tangent line to the parabola y = 4x – x2 at the point (1, 3) (i). using Definition 1 (ii). using Equation 2 (b). Find an equation of the tangent line in part (a). (c). Grap...

Q: (a). Evaluate h (x) = (tan x

(a). Evaluate h (x) = (tan x-x)/x3 for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005. (b). Guess the value of limx→0 tan x – x/x3. (c). Evaluate h (x) for successively smaller values of until you finally rea...

Q: Show that f is continuous on (-∞, ∞). /

Show that f is continuous on (-∞, ∞).

Q: (a). Use numerical and graphical evidence to guess the value

(a). Use numerical and graphical evidence to guess the value of the limit limx→1 x3 – 1/√x - 1 (b). How close to 1 does have to be to ensure that the function in part (a) is within a distance 0.5 of i...

Q: Find the numbers at which the function is discontinuous. At which

Find the numbers at which the function is discontinuous. At which of these points is continuous from the right, from the left, or neither? Sketch the graph of f.

Q: Use a graph to determine how close to 2 we have to

Use a graph to determine how close to 2 we have to take to ensure that x3 – 3x + 4 is within a distance 0.2 of the number 6. What if we insist that x3 - 3x + 4 be within 0.1 of 6?

Q: For what value of the constant is the function continuous f on

For what value of the constant is the function continuous f on (-∞, ∞)?

Q: Find the values of and that make continuous everywhere.

Find the values of and that make continuous everywhere.

Q: Which of the following functions f has a removable discontinuity at a

Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x ≠ a and is continuous at a.