Questions from General Calculus

Q: (a). How is the number e defined? (

(a). How is the number e defined? (b). Express e as a limit. (c). Why is the natural exponential function y = ex used more often in calculus than the other exponential functions y = ax? (d). Why is t...

Q: (a). Explain how implicit differentiation works. When should you

(a). Explain how implicit differentiation works. When should you use it? (b). Explain how logarithmic differentiation works. When should you use it?

Q: How do you find the slope of a tangent line to a

How do you find the slope of a tangent line to a parametric curve x = f (t), y = g (t)?

Q: Write an expression for the linearization of, f at a.

Write an expression for the linearization of, f at a.

Q: (a). What does it mean for f to be continuous

(a). What does it mean for f to be continuous at a? (b). What does it mean for f to be continuous on the interval (∞,∞)? What can you say about the graph of such a function?

Q: Which of the following curves have vertical asymptotes? Which have horizontal

Which of the following curves have vertical asymptotes? Which have horizontal asymptotes? (a). y = x4 (b). y = sin x (c). y = tan x (d). y = ex (e). y = ln x (f). y = 1/x (g). y = √x

Q: State the derivative of each function. (a). y

State the derivative of each function. (a). y = xn (b). y = ex (c). y = ax (d). y = ln x (e). y = logax (f). y = sin x (g). y = cos x (h). y = tan x (i). y = y = csc x (j). y = sec x (k). y = co...

Q: State the following Limit Laws. (a). Sum Law

State the following Limit Laws. (a). Sum Law (b). Difference Law (c). Constant Multiple Law (d). Product Law (e). Quotient Law (f). Power Law (g). Root Law

Q: If y = f (x) and x changes from x1

If y = f (x) and x changes from x1 to x2, write expressions for the following. (a). The average rate of change of y with respect to x over the interval [x1, x2]. (b). The instantaneous rate of change...

Q: Find the parabola with equation y = ax2 + bx whose tangent

Find the parabola with equation y = ax2 + bx whose tangent line at (1, 1) has equation y = 3x - 2.