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Vitek1552 [10]
3 years ago
12

Please solve Questions - 18 , 20 , 21 Show proper work. Thank-you!

Mathematics
1 answer:
Ymorist [56]3 years ago
3 0
18. If f(x)=[xsin πx] {where [x] denotes greatest integer function}, then f(x) is:
since x denotes the greatest integers which could the negative or the positive values, also x has a domain of all real numbers, and has no discontinuous point, then x is continuous in (-1,0).

Answer: B]

20. Given that g(x)=1/(x^2+x-1) and f(x)=1/(x-3), then to evaluate the discontinuous point in g(f(x)) we consider the denominator of g(x) and f(x). g(x) has no discontinuous point while f(x) is continuous at all points but x=3. Hence we shall say that g(f(x)) will also be discontinuous at x=3. Hence the answer is:
C] 3

21. Given that f(x)=[tan² x] where [.] is greatest integer function, from this we can see that tan x is continuous at all points apart from the point 180x+90, where x=0,1,2,3....
This implies that since some points are not continuous, then the limit does not exist.
Answer is:
A]


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Read 2 more answers
What is a polygonomial
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See below

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3 0
2 years ago
Write an equation for a circle with a diameter that has endpoints at (–10, 1) and (–8, 5). Round to the nearest tenth if necessa
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The standard form for the equation of a circle is :

<span><span><span> (x−h)^</span>2</span>+<span><span>(y−k)^</span>2</span>=<span>r2</span></span><span> ----------- EQ(1)
</span><span> where </span><span>handk</span><span> are the </span><span>x and y</span><span> coordinates of the center of the circle and </span>r<span> is the radius.
</span> The center of the circle is the midpoint of the diameter.

 So the midpoint of the diameter with endpoints at (−10,1)and(−8,5) is :

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  Now, use the distance formula to find the radius of the circle:

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 Subtituting h=−9, k=3 and r=√5 into EQ(1) gives :

 (x+9)^2+(y−3)^2=5

7 0
2 years ago
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