1.=9900
2.=9.3
3.= x= 12.2155
Hope this helps
(x^2+5x-36)/(x^2-16)
=(x^2+9x-4x-36)/(x^2-4^2)
=x(x+9)-4(x+9)/(x+4)(x-4)
=(x-4)(x+9)/(x+4)(x-4)
=x+9/x+4
Hope this helps.
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]
In my opinion I would use the mean. But the options that are given I would choose answer A. But I'm not 100% sure.
