Calculus

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

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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

EXPERT ANSWER

The enrollment at a small community college for the fall semester is 10% higher than the enrollment in the fall semester a year ago. The number of students increased by 5%, and the number of male students increased by 20%. Female students make up what portion of the current enrollment at the community college? Give your anser as a fraction.

The enrollment at a small community college for the fall semester is 10% higher than the enrollment in the fall semester a year ago. The number of students increased by 5%, and the number of male students increased by 20%. Female students make up what portion of the current enrollment at the community college? Give …

The enrollment at a small community college for the fall semester is 10% higher than the enrollment in the fall semester a year ago. The number of students increased by 5%, and the number of male students increased by 20%. Female students make up what portion of the current enrollment at the community college? Give your anser as a fraction. Read More »

Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. A 10- 6- 4 Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) O A. The function f(x) has a relative minimum at x = and has no relative maximum OB. The function f(x) has a relative maximum at x = and has no relative minimum. OC. The function f(x) has a relative minimum at x = and a relative maximum at x = 7 OD. There is not enough information given. O E. The function f(x) has no relative extrema. 2- 10-8 24 68 10 -2 – 6 -10

EXPERT ANSWER In this question given in above figure we use the first derivative test to find relative maximum and minimum. If the derivative f’ (x) changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. … When this technique is used to determine local …

Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. A 10- 6- 4 Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) O A. The function f(x) has a relative minimum at x = and has no relative maximum OB. The function f(x) has a relative maximum at x = and has no relative minimum. OC. The function f(x) has a relative minimum at x = and a relative maximum at x = 7 OD. There is not enough information given. O E. The function f(x) has no relative extrema. 2- 10-8 24 68 10 -2 – 6 -10 Read More »

Lim x-> infinity (1-(e^x))/(1+(2e(^x)))

Lim x-> infinity (1-(e^x))/(1+(2e(^x))) EXPERT ANSWER To find the lt –> infnity {(1-e^x)/(1+2e^x)}, we transform e^x = y and so when x–>ifinity, y = e^x –>ifinity. Therefore, Lt x–> ifinity {(1-e^x)/(1+2e^x)} = Lty–>infinity (1-y)/(1+2y) Lt x–> ifinity {(1-e^x)/(1+2e^x)} = Lty–>infinity (1-y)/(1+2y). We divide both numerator and denominator by y on the right: Lt x–> ifinity …

Lim x-> infinity (1-(e^x))/(1+(2e(^x))) Read More »

In these exercises, make reasonable assumptions about the graph of the indicated function outside of the region depicted. For the function g graphed in the accompanying figure, find lim x right 0- g(x) lim x rightarrow 0+ g(x) lim x rightarrow 0 g(x) g(0).

EXPERT ANSWER a) When x = 0, we are talkin about the y-axis And when they ask us to find the limit as x —> 0(-), we are looking at the value of y when x is approaching 0 from the negative side. Notice that at x = 0, y = 3. Also, when x …

In these exercises, make reasonable assumptions about the graph of the indicated function outside of the region depicted. For the function g graphed in the accompanying figure, find lim x right 0- g(x) lim x rightarrow 0+ g(x) lim x rightarrow 0 g(x) g(0). Read More »