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The Minimum Value Of 4e 2x 9e 2x Is

1) 11 2) 12 3) 10 4) 14 Solution: (2) 12 f (x) = 4e2x + 9e-2x f’ (x) = 8e2x - 18e-2x f '(x) = 0 8e2x - 18e-2x = 0 Taking... View Article

1) 2x + 3y = 3√2 2) 2x - 3y = 3√2 3) 3x + 2y = 3√2 4) 3x + 2y = 3√2 Solution: (3) 3x + 2y = 3√2 x = 2 cos3 θ x = 2 * (1 / 2 √2)... View Article

1) -1, 1 2) -2, 2 3) -3, 3 4) -4, 4 Solution: (1) -1, 1 4 cos (x2) cos [(π / 3) + x2] cos [(π / 3) - x2] = 4 cos (x2) [(1 / 2)... View Article

1) more than one minimum 2) exactly one minimum 3) at least one maximum 4) None of the above Solution: (2) exactly one minimum f... View Article

1) 20 2) 16 3) 24 4) 8 5) 4 Solution: x + 2y = 8 y = [8 - x] / 2 P = xy = [8x - x2] / 2 dP / dx = (1 / 2) (8 - 2x) = 0 8... View Article

1) (0, 0) 2) (0, a) 3) (a, 0) 4) (a, a) Solution: (2) (0, a) √x + √y = √a (1 / 2√x) + (1 / 2√y) y’ = 0 y’ = - √y / x Slope of... View Article

1) 2048/9 2) 2048/81 3) 2048/3 4) 2048/27 Solution: (4) 2048 / 27 x + y = 8 (x / 2) + (x / 2) + y = 8 [(x / 2) + (x / 2) + y] /... View Article

1) -4 2) 0 3) 1 4) 4 Solution: (4) 4 y = 2x3 - 3x2 - 12x + 5 y’ = 6x2 - 6x - 12 = 6 (x2 - x - 2) = 6 (x - 2) (x + 1) y’ = 0 at... View Article

1) it is a constant distance from the origin 2) it passes through (aπ/2, -a) 3) it makes π/2 - θ with the x-axis 4) it passes through... View Article

1) {x : -16 ≤ x < 16} 2) {x : -12 ≤ x < 12} 3) {x : -9 ≤ x < 9} 4) {x : 0 ≤ x < 10} Solution: (1) {x : -16 ≤ x < 16}... View Article

1) -1/4 2) 0 3) 1/4 4) 1/2 Solution: (2) 0 y = x40 - x20 y’ = 40 x39 - 20 x19 = 20x19 (2x20 - 1) = 0 x = 0, x20 = 1 / 2 y... View Article

1) 2 log a 2) 1/log a 3) log a 4) Solution: (2) 1 / log a y = ax y’ = ax ln a Length = y / y’ = ax / [ax ln a] = 1 / ln a... View Article

1) ST = SN 2) ST = 2SN 3) ST2 = aSN3 4) ST3 = aSN Solution: (1) ST = SN x = a (θ + sin θ) dx / dθ = a (1 + cos θ) y = a (1 - cos... View Article

1) πc / 6 2) πc / 4 3) 4c 4) 2c Solution: (4) 2c... View Article

1) (a, a) 2) (0, a) 3) (0, 0) 4) (a, 0) Solution: (3) (0, 0) x = at2, y = 2at When tangent to the curve is perpendicular to... View Article

1) x + y - 3 = 0 2) x + y - 1 = 0 3) x + y + 1 = 0 4) x + y + 3 = 0 Solution: (1) x + y - 3 = 0 x = t2 and y = 2t y2 = 4t2 = 4x... View Article

1) 1/ee 2) e 3) e1/e 4) 1/e Solution: (3) e1/e y = x1/x = e(1/x) ln x y’ = e(1/x) ln x [(1 / x) * (1 / x) + ln x (- 1 / x2)] =... View Article

1) a < 0, b > 0 2) a > 0, b < 0 3) a < 0, b < 0 4) Data is insufficient Solution: (1) a < 0, b > 0 (2) a >... View Article

1) (3 / 2, 13 / 2) 2) (- 5 / 2, - 17 / 2) 3) (3 / 2, 17 / 2) 4) (0, - 4) 5) (3 / 2, - 17 / 2) Solution: (5) (3 / 2, - 17 / 2) y... View Article

1) 4 2) 32 3) 8 4) 16 Solution: y = x2 - x + 4 Slope of the tangent P (1, 4) is dy / dx = 2x - 1 (dy / dx)1,4 = 2 - 1 = 1 The... View Article