Answer:
The simplest form is 1/r^7 + 1/s^12
Step-by-step explanation:
The given expression is r^-7+s^-12.
Notice that the exponents of both the base are negative
So, we will apply the rule which is:
a^-b = 1/a^b
Which means that to change the exponent into positive we will write it as a fraction:
r^-7+s^-12.
= 1/r^7 + 1/s^12..
Therefore the simplest form is 1/r^7 + 1/s^12....
Hope this helps you, and good luck in the future :)
Step-by-step explanation:
The ratio's can be expressed as fractions and you may compare those.
In order to compare fractions you need to bring them into equal denominator.
8 and 9 have LCM of 8*9 = 72 since they have no common factors.
<u>The equivalent fractions with common denominator are:</u>
- 5/8 = 9*5/(9*8) = 45/72
- 7/9 = 8*7/(8*9) = 56/72
<u>Now we can compare the fractions:</u>
- 45/72 < 56/72, since 45 < 56
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]
