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Elenna [48]
3 years ago
11

PLEASE HELP, I WILL MOVE TO A DIFFERENT SCHOOL IF I DONT PASS!!!!

Mathematics
1 answer:
Mkey [24]3 years ago
5 0
Is there a picture i could see or something?
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Discuss the continuity of the function on the closed interval.Function Intervalf(x) = 9 − x, x ≤ 09 + 12x, x > 0 [−4, 5]The f
quester [9]

Answer:

It is continuous since \lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)

Step-by-step explanation:

We are given that the function is defined as follows f(x) = 9-x, x\leq 0 and f(x) = 9+12x, x>0 and we want to check the continuity in the interval [-4,5]. Note that this a piecewise function whose only critical point (that might be a candidate of a discontinuity)  x=0 since at this point is where the function "changes" of definition. Note that 9-x and 9+12x are polynomials that are continous over all \mathbb{R}. So F is continous in the intervals [-4,0) and (0,5]. To check if f(x) is continuous at 0, we must check that

\lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x) (this is the definition of continuity at x=0)

Note that if x=0, then f(x) = 9-x. So, f(0)=9. On the same time, note that

\lim_{x\to 0^{-}} f(x) = \lim_{x\to 0^{-}} 9-x = 9. This result is because the function 9-x is continous at x=0, so the left-hand limit is equal to the value of the function at 0.

Note that when x>0, we have that f(x) = 9+12x. In this case, we have that

\lim_{x\to 0^{+}} f(x) = \lim_{x\to 0^{+}} 9+12x = 9. As before, this result is because the function 9+12x is continous at x=0, so the right-hand limit is equal to the value of the function at 0.

Thus, \lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)=9, so by definition, f is continuous at x=0, hence continuous over the interval [-4,5].

5 0
3 years ago
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Which unit would you use to measure the amount of milk in a half-gallon carton?
Jlenok [28]
You would use L to measure the amount
3 0
3 years ago
If 6 is added to the square of an integer, the result is 3 less than 10 times that integer. Find the integer(s).
zhannawk [14.2K]

Answer:

1 is the original integer

Step-by-step explanation:


6 0
3 years ago
In a triangle Labled PQR, R is 35 degrees less than P and P is 16 degrees greater than Q. What are the measures of the angles? L
Ludmilka [50]

Answer:

55

Step-by-step explanation:

in triangle PQR,

PQ=PR. Therefore PQR is an isosceles triangle.

therefore, angle Q= angle R(because angles opposite to equal sides of an isosceles triangle are equal)

angle P +angle Q + angle R= 180°(angle sum property)

2*angle Q + angle P = 180°(angle Q= angle R)

2*angle Q=180°-70°

angle Q= 110°/2

angle Q=55°=angle R

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2 years ago
Eric has been donating books he no longer needs to his local library. After 3 months of donating, he had 157 books left in his r
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He donated about eleven books per month.
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