Evaluate \(\int \sin 3x \mathrm d x\)
(2/3) cos 3x + c
(1/3) cos 3x + c
(-1/3) cos 3x + c
(-2/3) cos 3x + c
Correct answer is C
\(\int \sin 3x \mathrm d x = - \frac{\cos 3x}{3} + c\)
= \(-\frac{1}{3} (\cos 3x) + c\)
The slope of the tangent to the curve y = 3x\(^2\) - 2x + 5 at the point (1, 6) is
4
1
6
5
Correct answer is A
y = 3x\(^2\) - 2x + 5
Slope = \(\frac{\mathrm d y}{\mathrm d x} = 6x - 2\)
At x = 1,
Slope : 6(1) - 2 = 4.
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.
10 sin 5x cos 5x
5 sin5x cos 5x
2 sin 5x cos 5x
15 sin 5x cos 5x
Correct answer is A
\(y = \sin^{2} (5x)\)
Let u = sin 5x
\(\frac{\mathrm d u}{\mathrm d x} = 5 \cos 5x\)
\(\therefore y = u^{2}\)
\(\frac{\mathrm d y}{\mathrm d u} = 2u\)
\(\frac{\mathrm d y}{\mathrm d x} = 2u . 5 \cos 5x\)
= \(10u \cos 5x\)
= \(10 \sin 5x \cos 5x\)
If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x.
2x2 - 3x
x2 - 3x
x2 - 3x - 3
x2 - 3x + 3
Correct answer is D
dy/dx = 2x - 3
y = ∫2x - 3 dx => y = x2 - 3x + c
3 = (0)2 - 3(0) + c
=> c = 3
Thus y = x2 - 3x + 3
60
50
45
36
Correct answer is A
Let the number of goats be X
C.P of X goats = N4000X
S.P of X goats = (75/100) x 4000X = N3000X
3000X = 180,000
=> X = 180000/3000 = 60.
X = 60 goats