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nataly862011 [7]
2 years ago
10

HELP !!!. I need help with these questions( see image). Please show workings.

Mathematics
1 answer:
snow_lady [41]2 years ago
6 0

9514 1404 393

Answer:

  • a) 7
  • b) -27
  • c) 18
  • d) 8
  • e) 2
  • f) 1

Step-by-step explanation:

The limit of any polynomial function at a point is the value of the polynomial at that point. A polynomial is defined and continuous for all values of the independent variable.

The limit of a rational function at a "hole" is the value of the simplified function at that point.

1a) lim = 4+3+2-2 = 7

1b) lim = (3)(-3)(3) = -27

1c) lim = 3^2+9 = 18

1d) lim = (x+4) = 4+4 = 8

1e) lim = 3x+1 = 3(1/3) +1 = 2

1f) lim = x^2/x^2 = 1

_____

The expressions of (e) and (f) can be simplified by factoring the difference of squares: a^2 -b^2 = (a -b)(a +b). In each case, one of the factors cancels the one in the denominator, so the remaining function can be evaluated at the limit point.

As x approaches infinity, the only terms of a rational expression that matter are those of the highest degree in numerator and denominator. (There's a little more to it if the numerator has a higher degree than the denominator.)

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If I have x cars and sell 12 how many cars do I have left.

Step-by-step explanation:

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Show how you round 1345/99 to the nearest integer
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14

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When simplified, the algebraic expression (2 a - 3 b ) 2 is a binomial.<br><br><br> True or False
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Anna's car requires 5 1/2 gallons of gasoline to make 4 round trips to work and back. If her car can travel 24 miles per gallon
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4 0
2 years ago
Which is an equation of the line that contains the points (0,2) (4,0)
alekssr [168]

Answer:

Y= -1/2x+2

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m=

0 - 2

4 - 0

or...

m=

-2

4

or...

m=-1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(4,0). When x of the line is 4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-1/2x+b. b is what we want, the -1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=-1/2 × 0+b, or solving for b: b=2-(-1/2)(0). b=2.

(4,0). y=mx+b or 0=-1/2 × 4+b, or solving for b: b=0-(-1/2)(4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (4,0)

is

y=-1/2x+2

4 0
3 years ago
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