Questions from General Calculus

Q: Find f ‘(x). Check that your answer is reasonable by

Find f ‘(x). Check that your answer is reasonable by comparing the graphs of f and f ‘. f(x) = arctan (x2 – x)

Q: The figure shows a lamp located three units to the right of

The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x2 + 4y2 ≤ 5. If the point (-5, 0) is on the edge of the shadow, how far above the...

Q: A model for the concentration at time t of a drug injected

A model for the concentration at time t of a drug injected into the bloodstream is C(t) = K(e-at – e-bt) where a, b, and K are positive constants and b > a. Sketch the graph of the concentration funct...

Q: (a) Find y’ by implicit differentiation. (b

(a) Find y’ by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get y’ in terms of x. (c) Check that your solutions to parts (a) and (b) are consistent by substit...

Q: Show that the curve y = x – tan-1x has

Show that the curve y = x – tan-1x has two slant asymptotes: y = x + π/2 and y = x - π/2. Use this fact to help sketch the curve.

Q: (a) Find y’ by implicit differentiation. (b

(a) Find y’ by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get y’ in terms of x. (c) Check that your solutions to parts (a) and (b) are consistent by substit...

Q: Show that the lines y = (b/a)x

Show that the lines y = (b/a)x and y = -(b/a)x are slant asymptotes of the hyperbola (x2/a2) – (y2/b2) = 1.

Q: Use the asymptotic behavior of f (x) = sin x

Use the asymptotic behavior of f (x) = sin x + e-x to sketch its graph without going through the curve sketching procedure of this section.

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f ’ and f ’’ to estimate the intervals of increase and decrease, extreme values, interva...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f ’ and f ’’ to estimate the intervals of increase and decrease, extreme values, interva...