Calculus

The function w gives the number of words per minute (wpm) that a student in a keyboard class can type after t weeks in the course. (a) Is it possible for w(3) to be negative? Explain. W(3) cannot be negative because the lowest number of words typed in a minute is 1 x ? dt t = 3 (b) What are the units on dw O weeks O weeks per wpm wpm per week wpm (c) Is it possible for dw dt to be negative? Explain. t = 3 dw dt can be negative because the number of words typed per minute can decrease at week 3. t = 3

Mathematics, Calculus / By

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EXERCISE SET 2.5 Graphing Utility 1-18 Find f ‘(x). Er wobere seconds 5 olan sd 15.) (1f(x) = 4 cos x + 2 sin x 2. f(x) = 2 + sin x d i 3. f(x) = -4×2 cosx 4. f(x) = 2 sin² x f(r) – 3 – Cos xps 10r ) sin x o s 5+ sin x x2 + sin x (7. f(x) = sec x – V2 tan x 8. f(x) = (x2 + 1) sec x 9. f(x) = 4 csc x – cotx 10. f(x) = cos x – x csc x 11. f(x) = sec x tan x 12. f(x) = csc xcot x 13. f(x) = cotx 14. f(x) = sec x 1 + csc x (15. f(x) = sin’ x + cos²x 1 + tan x 16. f(x) = sec? x – tan” x (x² + 1) cotx 18. f(x) = 3 – COS X CSC X 17. f(x) = sin x sec x 1 + x tan x

Mathematics, Calculus / By

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Consider RL-circuit R wwww ups. E 1. Determine the differential equation governing the current I (in amperes) on the circuit. av 2. Solve the equation to find the current in the case of constant electromotive force E(t) = E, constant. Evaluate the constant of integration by using the condition I(0) Io. = 3. Determine the limit lim I(t) where I (t) is obtained form the above question. 1-00 4. Let R = 100 ohms, L = 2.5 henries, E(t) = 110 cos 314t. Find the steady-state solution. eeee

Calculus, Mathematics / By

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