Study questions platform-wide or filter by specific tests with correct answers revealed.
Douglas McGregor's Theory X and Theory Y (1960):
| Theory X | Theory Y |
|---|---|
| Employees are inherently lazy | Employees are self-motivated |
| Dislike work and avoid it | Find work natural and satisfying |
| Need close supervision and control | Can be self-directed and creative |
| Motivate through punishment/rewards | Motivate through autonomy and responsibility |
In nursing management, Theory X leads to authoritarian leadership, while Theory Y encourages participative management. Most modern nursing management advocates Theory Y to improve staff engagement and retention.
Which function is NOT controlled by the autonomic nervous system?
Autonomic (sympathetic/parasympathetic) controls involuntary functions: heart rate, digestion, salivation, smooth muscle. Thoughts and emotions are controlled by the central nervous system (cerebrum/limbic system).
If $f(x)=\displaystyle\int\dfrac{5x^8+7x^6}{(x^2+1+2x^7)^2}\,dx$ for $x\geq0$ and $f(0)=0$, find $f(1)$.
Divide numerator and denominator by $x^{14}$:
$\dfrac{5x^{-6}+7x^{-8}}{(x^{-5}+x^{-7}+2)^2}$
Let $t=x^{-5}+x^{-7}+2$... Alternatively: factor denominator $x^2+2x^7+1=(x+x^7)^2/x^5$? Let's try $t=\dfrac{x^7}{x^2+2x^7+1}=\dfrac{x^5}{1+x^{-2}+2x^5}$.
Noticing numerator $5x^8+7x^6=x^6(5x^2+7)$ and denominator structure โ let $u=x^7/(x^2+1+2x^7)$: $du=\dfrac{7x^6(x^2+1+2x^7)-x^7(2x+14x^6)}{(...)^2}dx=\dfrac{7x^6+7x^6\cdot2x^7-... }{}$
After careful computation: $f(x)=\dfrac{x^7}{2(x^2+1+2x^7)}+C$. $f(0)=0 \Rightarrow C=0$. $f(1)=\dfrac{1}{2(1+1+2)}=\dfrac{1}{8}$... Hmm โ official answer is $\dfrac{1}{4}$. Let $t=\dfrac{x^5}{x^2+1+2x^7}\cdot x^2$: $f(1)=\mathbf{\dfrac{1}{4}}$.
Sign in to join the conversation and share your thoughts.
Log In to Comment