x2 - sin x + c
x2 + sin x + c
x2/2 - sin x + c
x2/2 + sin x + c
Correct answer is D
dy/dx = x + cos x
y = ∫(x + cos x)dx
y = 1/2x2 + sin x + C
Find the value of x for which the function 3x\(^3\) - 9x\(^2\) is minimum
zero
2
3
5
Correct answer is B
y = 3x\(^3\) - 9x\(^2\)
dy/dx = 9x\(^2\) - 18x
As dy/dx = 0
9x\(^2\) - 18x = 0
9x(x-2) = 0
9x = 0 which implies x = 0
x-2 = 0 implies x = 2
d2y/dx2 = 18x - 18
when x = 0
d2y/dx2 < 0 ∴ x is is minimum
when x = 2d\(^2\)y/dx\(^2\) = 18
∴ the value > 0 x is minimum
Differentiate (x2 - 1/x)2 with respect to x
4x2 - 4x - 2/x
4x2 - 2 + 2/x3
4x2 - 2 - 2/x3
4x2 - 3x + 2/x
Correct answer is C
y = (x2 - 1/x)2
y = (x2 - 1/x)(x2 - 1/x)
y = x4 - x - x + 1/x2
y = x4 - 2x + 1/x2
y= x4 - 2x + x-2
dy/dx = 4x2 - 2 - 2x-3
= 4x2 - 2 - 2/x3
y = x2 + 7x + 9
y = x2 + 7x - 18
y = x2 + 7x + 18
y = x2 + 14x + 11
Correct answer is B
dy/dx = 2x + 7
y = ∫2x + 7
y = x2 + 7x + C at (2,0)
0 = 22 + 7(2) + C
0 = 4 + 14 + C
0 = 18 + C
C = -18
∴ The equation is y = x2 + 7x - 18
For what of n is n+1C3 = 4(nC3)?
6
5
4
3
Correct answer is D
\(^{n+1}C_3 = 4(^nC_3)\\\frac{(n+1)!}{(n+1-3)!3!} = 4\left(\frac{n!}{(n-3)!3!}\right)\\\frac{(n+1)n!}{(n-2)(n-3)!}=4\left(\frac{n!}{n-3!}\right)\\=\frac{n+1}{n-2}=\frac{4}{1}\\n+1 = 4(n-2)\\n+1 = 4n-8\\-3n = -9\\\frac{-9}{-3}\\n=3\)