15o
30o
45o
60o
Correct answer is C
30 + 45 + 60 + 90 + 2x + x = 360°
225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45°
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\)
zero
1
2
3
Correct answer is C
\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\
=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\)
= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2
Evaluate \(\int_1 ^2(6x^2-2x)dx\)
16
13
12
11
Correct answer is D
\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\
= [2x^3 - x^2]_1^2\)
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
Find the minimum value of the function y = x(1+x)
-1/4
-1/2
1/4
1/2
Correct answer is A
y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4
x cos x
x sin x
-x cos x
-x sin x
Correct answer is B
sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x