A. (x, y) → (x, y + 4)

Mathematics

1 answer:

Harrizon [31]2 years ago

3 0

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Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit

soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

continuous at x=4? Why or why not? Choose the correct answer below.

Answer:

(D) Yes, f(x) is continuous at x = 4 because $Lim_{x \to 4}f(x)=f(4)$

Step-by-step explanation:

Given the function:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

A function to be continuous at some value c in its domain if the following condition holds:

f(c) exists and is defined.

$Lim_{x \to c}$ f(x)$ exists.

$f(c)=Lim_{x \to c}$ f(x)$

At x=4

$f(4)=\dfrac{1}{4}*4+1=2$

$Lim_{x \to 4}f(x)=2$

Therefore: $Lim_{x \to 4}f(x)=f(4)=2$

By the above, the function satisfies the condition for continuity.

The correct option is D.

3 0

2 years ago

I need help asap!!!!!

tino4ka555 [31]

Answer:34

Step-by-step explanation:

6 0

3 years ago

Can I get help on this please

Alekssandra [29.7K]

Hello!

I've attached the diagram.

For this problem, since you have a right triangle, you can use the Pythagorean Theorem to fine the length of the ladder (the hypotenuse of the triangle).

Pythagorean Theorem (where c is the hypotenuse):
a² + b² = c²

The triangle's leg lengths are 8 and 6; substitute into the theorem:
8² + 6² = c²

Simplify:
64 + 36 = c²
100 = c²
10 = c

Answer:
The length of the ladder is 10 m.