
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>

</span><span>In notation we write respectively
</span>

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence

Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²

That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers 
Answer:
39 degrees
Step-by-step explanation:
The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP. Take 180-141 to get 39 degrees for <PMN
What is the solution to 3 + 4e^x+1 = 11?
Solution:

To solve for x, Let us subtract 3 from both sides



Let us divide by 4 on both sides



Let us take ln on both sides

So, x+1=ln(2)
To solve for x, Let us subtract 1 from both sides
x+1-1=ln(2) -1
x+0=ln(2)-1
x= ln(2) -1
Answer: Option (A)
x=ln(2)-1