Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
\(\frac{5}{8}\)
\(\frac{5}{6}\)
\(\frac{5}{4}\)
\(\frac{5}{2}\)
Correct answer is C
(1 + \(\frac{1}{2} x )^5\)
1(1)\(^3\)(\(\frac{1}{2} x)^0\) - 5(1)\(^4\)(\(\frac{1}{2} x)^1\)
+ 10 (10)\(^3\)(\(\frac{1}{2} x )^2\) + 10(1)\(^2\) (\(\frac{1}{2} x\))\(^3\)
Coefficient of x\(^3\)
10(\(\frac{1}{2} x)^3\) = \(\frac{10}{8} x^3\) =
= \(\frac{5}{4}\)
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
N = X\(^{\frac{v}{p}}\) - M
N = X\(^{\frac{p}{v}}\) - M
N = X\(^{\frac{v}{p}}\) + M
N = X\(^{\frac{p}{v}}\) + M
Correct answer is A
\(\frac{v}{p} = \frac{p}{p} log _x(M + N)\)
\(\log_x(M + N) = \frac{v}{p}\)
\(x^{\frac{v}{p}} = M + N\)
N = X\(^{\frac{v}{p}}\) - M
Given that 2x + 3y - 10 and 3x = 2y - 11, calculate the value of (x - y).
5
3
-3
-5
Correct answer is D
2x + 3y = 10 .......x2
3x - 2y = -11 ........x3
4x + 6y = 20
9x - 6y = -33
\(\overline{\frac{13x}{13} = \frac{-13}{13}}\), x = 1
from
2x + 3y = 10
2(-1) + 3y = 10
-2 + 3y = 10
3y = 10 + 2
\(\frac{3y}{3} = \frac{12}{3}\), y = 4
x - y = -1 - 4
= -5
Differentiate \(\frac{x}{x + 1}\) with respect to x.
\(\frac{x}{x + 1}\)
\(\frac{-1}{x + 1}\)
\(\frac{1 - x}{(x + 1)^2}\)
\(\frac{1}{(x + 1)^2}\)
Correct answer is D
\(\frac{d}{dx}(\frac{x }{x + 1}\)) = \(\frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}\)
u = x, \(\frac{du}{dx}\) = 1, v = x + 1, \(\frac{dv}{dx}\) = 1
= \(\frac{(x + 1)(1) - x (1)}{(x + 1)^2}\)
= \(\frac{x + 1 - x}{(x + 1)^2}\)
= \(\frac{1}{(x + 1)^2}\)
If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k.
- 21
- 22
- 24
- 25
Correct answer is B
\(\frac{6x + k}{2x^2 + 7x - 15} = \frac{4}{x + 5} - \frac{2}{2x - 3}\)
6x + k = 4 (2x - 3) - 2(x + 5)
6x + k = 8x - 12 - 2x - 10
6x + k = 6x - 22
k = - 22