9. Consider a pattern that begins with 28 and each consecutive number is six more than the previous term. What are the first thr
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Answer:
Step-by-step explanation:
The slope-intercept form is y=mx+b, where m is the slope and b is the y-coordinate of the y-intercept, so we can already conclude that b=-1.
This results in y = mx - 1
We also have the x-intercept, and we know that the y-coordinate of an x-intercept is always 0. This means that we have the point (4,0). Substitute this into the formula to generate m:
0 = 4m - 1
4m = 1
m = 1/4
thus y = x - 1
A) This particular limit is of the indeterminate form,
if we plug in infinity directly, though it is not a number just to check.
If a limit is in this form, we apply L'Hopital's Rule.
's
So we take the derivatives and obtain,
Still it is of the same indeterminate form, so we apply the rule again,
This simplifies to,
b) This limit is also of the indeterminate form,
we still apply the L'Hopital's Rule,
When we plug in zero now we obtain,
c) This also in the same indeterminate form
It is still of that indeterminate form so we apply the rule again, to obtain;
Now we have remove the discontinuity, we can evaluate the limit now, plugging in zero to obtain;
This gives us;
d)
For this kind of question we need to rationalize the radical function, to obtain;
We now divide both the numerator and denominator by x, to obtain,
This simplifies to,
if we plug in infinity directly, though it is not a number just to check.
If a limit is in this form, we apply L'Hopital's Rule.
's
So we take the derivatives and obtain,
Still it is of the same indeterminate form, so we apply the rule again,
This simplifies to,
b) This limit is also of the indeterminate form,
we still apply the L'Hopital's Rule,
When we plug in zero now we obtain,
c) This also in the same indeterminate form
It is still of that indeterminate form so we apply the rule again, to obtain;
Now we have remove the discontinuity, we can evaluate the limit now, plugging in zero to obtain;
This gives us;
d)
For this kind of question we need to rationalize the radical function, to obtain;
We now divide both the numerator and denominator by x, to obtain,
This simplifies to,