MCQ
In graphical solutions of linear inequalities, solution can be divided into.
- AOne subset
- BTwo subsets
- CThree subsets
- DFour subsets
Solution:
In graphical solutions of linear inequalities, solution can be divided into two subsets.
for example, $2\text{x}+\text{y}\leq4$
One subset includes all values (x, y) that satisfy the equation 2x + y = 4 and the other subset includes all the values (x, y) that satisfy 2x + y < 4.
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$I.$ $f$ has a zero in $(0,1)$
$II.$ $f$ is monotone in $(0,1)$ Then,
$f(x)=x \cos \frac{1}{x}, \quad x \geq 1,$
$(A)$ for at least one $x$ in the interval $[1, \infty), f(x+2)-f(x)<2$
$(B)$ $\lim _{x \rightarrow \infty} f^{\prime}(x)=1$
$(C)$ for all $x$ in the interval $[1, \infty), f(x+2)-f(x)>2$
$(D)$ $f^{\prime}(x)$ is strictly decreasing in the interval $[1, \infty)$