We have a domain of a function, that is, which x-es can we throw in. But we are asking which y-s will we get given that we can only throw x-es in $(-\infty,4)$ .

Let's try $x=4$ even though we are forbidden to put 4 inside $h$ we are still able to do so.

So $h(4)=0.5\cdot4-1=2-1=1$ what we just got is the upper limit of the range. The lower limit is $h(-\infty)=-\infty$ .

So the range is just $(-\infty, 1)$ .

Hope this helps :)

6 0

2 years ago

Calculate X3 dx . A.×2 + c B. 3X2 + c c . x4 + c D . x4/4+c

olga nikolaevna [1]

$\LARGE \int x^3 dx = \frac{x^4}{4}+C$

So the answer is choice D. You can check this by differentiating the right hand side and you'll get x^3 back again.

This answer can be found by using the power rule for integrals. That rule is

$\LARGE \int x^n dx = \frac{x^{n+1}}{n+1} + C$

4 0

3 years ago