Explanation:
Steve correctly computed the change in x to be 2, and the change in y to be 6. However he put 2 in the slope formula for Δy (the change in y), and 6 for Δx. That is, Steve reversed the values of Δx and Δy.
The actual slope is ...
slope = Δy/Δx = 6/2 = 3
Answer:
2. a and b only.
Step-by-step explanation:
We can check all of the given conditions to see which is true and which false.
a. f(c)=0 for some c in (-2,2).
According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.
b. the graph of f(-x)+x crosses the x-axis on (-2,2)
Let's test this condition, we will substitute x for the given values on the interval so we get:
f(-(-2))+(-2)
f(2)-2
-1-1=-3 lower limit
f(-2)+2
1+2=3 higher limit
according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.
c. f(c)<1 for all c in (-2,2)
even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.
The final answer is then 2. a and b only.
Answer:
Step-by-step explanation:
By the time you factorize this, you will get
x = 5.9521078984053 or <span>-2.3521078984053
</span>Please mark me as brainliest.
Assuming the series is
The series will converge if
We have
So the series will certainly converge if
, but we also need to check the endpoints of the interval.
If
, then the series is a scaled harmonic series, which we know diverges.
On the other hand, if
, by the alternating series test we can show that the series converges, since
and is strictly decreasing.
So, the interval of convergence for the series is
.
