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pishuonlain [190]
3 years ago
7

Please help! thanks so much​

Mathematics
1 answer:
Stels [109]3 years ago
4 0

Answer:

See below.

Step-by-step explanation:

First, we can see that \lim_{x \to 2}  (f(x))= -1.

Thus, for the question, we can just plug -1 in:

\lim_{x \to 2} (\frac{x}{f(x)+1})=\frac{(2)}{-1+1}  =und.

Saying undefined (or unbounded) will be correct.

However, note that as x approaches 2, the values of y decrease in order to get to -1. In other words, f(x) will always be greater or equal to -1 (you can also see this from the graph). This means that as x approaches 2, f(x) will approach -.99 then -.999 then -.9999 until it reaches -1 and then go back up. What is important is that because of this, we can determine that:

\lim_{x \to 2} (\frac{x}{f(x)+1})=\frac{(2)}{-1+1}  = +\infty

This is because for the denominator, the +1 will always be greater than the f(x). This makes this increase towards positive infinity. Note that limits want the values of the function as it approaches it, not at it.

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Step-by-step explanation:

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The derivative f ' of function f is defined ascthe above pic.

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3 0
2 years ago
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Can somebody help me plz plz
Paul [167]

Answer:

a. Function; every x-value corresponds to only 1 y-value

b. Not a function; doesn't pass the VLT

c. Function, passes the VLT

2.

a. -200

b. x= -22.5

Step-by-step explanation:

Here is the basic rule for a function:

Every input (x) value goes only to one output (y) value.

For example, an x-value of 4 cannot go to y-values of both 2 and 4. {(4,2), (4,4)

a.

In a, we see that every x value has only one line- no x-value goes to two different y values, therefore, a is a function.

b. Remember that every x-value can only have one matching y value. This definition allows us to do a special test called the vertical line test (VLT). If we pass a vertical line through a graph (|) and it doesn't pass through two points at the same x value, then that graph is a function.

However, in this graph we can clearly see that this function DOES NOT pass the VLT.

(-2, 2) and (-2,-3)

c.

We're going to use the VLT once again. If we put a vertical line through the observable graph does any x value appear to have two or more y-values? No, so this is the graph of a function

2.

g(x)= 16 -4x

g(54) is the same as saying input 54 in for x, so

16- 4(54)

16- 216 = -200

a. -200

b.

So, g(x) = 106 and they want you to determine x.

Set g(x) equal to 106 and solve:

106= 16-4x

90 = -4x

x= -22.5

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given the expression \dfrac{1}{(x-1)(x-9)}, we are to write the expression as a partial fraction. Writing as a partial fraction means rewriting the expression a s a sum of two or more expression.

Before we will do this we will need to check the nature of the function at the denominator whether it is linear, quadratic or a repeated function. According to the question, the denominator at the denominator is a linear function and since it is a linear function, we can separate both linear function without restriction as shown;

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