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(1) Solve the following differential equation. (8 pts.) dy ...

(1) Solve the following differential equation. (8 pts.) dy = (8r++3)e-34, = da (2) Find the area of the surface obtained by rotating the curve given by f3 x (t) =t T3, y(t) = t2. , 0 < t < 2 about the x-axis. (8 pts.) (3) A bacteria culture doubles in size every 5 hours, how long...

1. Determine whether or not the alternating series converge ...

1. Determine whether or not the alternating series converge or diverge. (-1) n+1 (a) n=1 2. Determine whether the series converges absolutely, or converges conditionally, or diverges and give reasons for your conclusions. (a) (-1)" 00 n=1 3n + 4 00 (b) (-0.2)" n=1 3. U...

10.6 In problems 17 31 determine whether the given series c...

10.6 In problems 17 31 determine whether the given series converge or diverge. 80 20. (-0.99) n+1 n=5 10.7 In problems 1 30 determine whether the given series Converge Absolutely, Converge Conditionally, or Diverge and give reasons for your conclusions. 00 1 4. [ (-1) n 2 + In(n) n=1 10....

As you have learned this semester, there are many different ...

As you have learned this semester, there are many different techniques of integration designed to handle different types of functions and situations As you have seen. some are harder than others. You have not seen every technique available and there are some problems that have no antiderivatives ...

A tank holds 2000 gallons of water, which drains from the bo...

A tank holds 2000 gallons of water, which drains from the bottom of the tank In half an hour. The values In the table show the volume V of water remaining In the tank (In gallons) after t minutes. t (min) 5 10 15 20 25 30 V (gal) 1392 870 480 214 58 Exercise (a) If P is the point (15,...

a Let SCIR3 be Jordan-measurable - with its "borde...

a Let SCIR3 be Jordan-measurable - with its "border" being the surface S= as which IS pieceurse smooth Deduce a formula for the volume of SL by using ch integral over the surface S for a certain field F. 2 Let SCIR3 be the sphere of raduus r with center at the origin and 20...

(1) For the function f(x) = 1 x²+1 (a) Find the deriv...

(1) For the function f(x) = 1 x²+1 (a) Find the derivative of f(x) (b) Find the domain of f(x) (c) Find the domain of f' (x) (2) Find the limit: limx 8 1 +4x4-2x - (3) Find derivative: dx d = dx d = = dx d = (2x - 3)2 (1 + tan (x2)) = ;; da dx d = and sin x e-x = (4) Find the antideriva...

1. (10 marks) Given that a, b, c > 0 find the maximu...

1. (10 marks) Given that a, b, c > 0 find the maximum of f(x,y, = raybe subject to the condition that x + y + 2 = 1 where x, y, 2 > 0. 2. (10 marks) Determine whether the vector field F = - - is conservative or not. If so or otherwise evaluate l' where r is the curve of interse...

10.1 Inproblems 7- 18, calculate the first 6terms (starting...

10.1 Inproblems 7- 18, calculate the first 6terms (starting withn= 1)of each sequence and graph these terms. 12. In problems 29 43, state whether each sequence converges or diverges. If the sequence converges find its limit. 30. {n2} 10.2 Inproblems 19-28, represent each repeating decimal as ...

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