Question
Thanx
Determine int dx/x1/5 + 2 The correct alternative is 5[1/4x4/5 - 2/3x3/5 + 4x2/5 - 81/5 + ln |x1/5 + 2|] + k 5[1/4x4/5 - 2/3x3/5 + 2x2/5 - 8x1/5 + 16ln |x1/5 + 2|] + k 5[1/4x4/5 - 1/3x3/5 - 4x2/5 + 81/5 + 16ln |x1/5 + 2|] + k None of the above. Determine the integral int dx/(4 -)3 The correct alternative is - 1/2 (4 - x)2 + k 2 / (4 - x)2 + k 1/2 1/ (4 - x)2 + k Not one of the above. Let f(x) = -sinx x epsilon [-pi/4, pi/6] The area between the graph of f and the x-axis is given by 2/ - - 1/ 1/ - 2/ 2 - . Evaluate the area between the curves y = x2 - 6 and y = -|x| The correst answer is 32 units2 -44/3units2 44/3units2 -32 units2 Determine the definite integral ln (log2 t)/ t ln t dt The correct alternative is (ln 2)2/2 - ln (ln 2) ln (ln 2)2 - 2ln2 -2 ln (ln 2) + (ln 2)2/2 (ln 2)2/2 - ln (ln 2) (ln 2) Solve the following initial-value problem for y as a function of x. dy/dx = 2/x2 + 6x + 10 y(0) =0 The correct answer is y = 2 tan-1 (x + 3) - 2 tan-1 (3) y = 2 arctan (x + 3) + 3 arctan(2) y = 2 tan-1 3 + 2 tan (x + 3) Not one of the above. Let w = ex/y + ez/x with x = ln u/v y = uv z=ln u/uv Find the value of partial w/partial u when u = 2 and v = 1. The correct answer is root2(1 - ln 2)/4 root2/4 + root2 ln 2/4 ln 2-1/root2 Not one of the above. Write a Chain Rule formula for partial w/partial z if w = f(x, y), y = g(x, z) x = h(z). partial w/partial z = partial w/partial x partial x/partial z + partial w/partial x partial x/partial z + partial y/partial z partial w/partial z = partial w/partial x partial x/partial z + partial w/partial x partial x/partial z + partial w/partial y partial y/partial z partial w/partial z = partial w/partial x partial x/partial z + partial w/partial y partial y/partial x partial x/partial z + partial w/partial y partial y/partial z Note one of the above. Let y(x) = ln tdt Use the Fundamental Theorem of Calculus to evaluate dy/dx. The correct alternative is 2xe2x + 27xe3x -4xe2x + 9xe3x ln |e2x| e2x 2 + ln |e3x| 3 Not one of the above. Use implicit differentiation to evaluate dy/dx when tan (xy2) + 3y = 2xy. The correct alternative is dy/dx = 2y - y2 sec2 (xy2)/2xysec2 (xy2) - 2x + 3 dy/dx = 3 - 2y - y2 sec2 (xy2)/2xy sec2 (xy2) - 2x dy/dx = 2y + y2 sec2 (xy2)/-2xy sec2 (xy2) + 2x - 3 Not one of the above.
Explanation / Answer
11-2
12-3
13- 4
14-3
15-4
16-1
17-2
18-2
19-2
20-3
