Question

True of False (dont need to solve)

1. _____According to the L’hospital’s rule, lim(x-->a) f(x)/g(x)= L if f'(x)/g'(x)=L
2. _____ A monotonically increasing function cannot have a max or min in a closed interval [a, b] because f’(x) >0 for all x in (a, b).
3. _____ For x>10, the ratio ln(x)/sqrt(x-10) approaches 0 as x --> infinity .
4. _____ lim(x-->infinity) (3x^3 +12x^2 -8x +1)/(x^2 + 2)(3x-1) =3
5. _____
6. _____ x = -1 is an asymptote of y= 1/(sqrt(x+1))
7. _____
8. _____ y=0 is an asymptote for y=1/x.
9. _____ y=7/5 is an asymptote for y= 7x+1/(5x-8)

Answer 1

9 1) False (n) man. Cannot have at > According to l'Hospital's rule it f(x)=L it 8' (*)/9'6") =< 1*%'(a) / 9' (a) = L) 2) False A monotonically increasing function ol min. in acclosed interval [a, b] because I'ln) > 0 for all rin (a,b) (manimam value x=b and minimum value at x = a because function is increasing.) 3) Prue nalo the ratio enx/50-To approaches to end ym 252-10 1/250-10 ashri-10 x su 3n² + 12 n² – 8 ntl - it x 3 +128 -8 2 + 1 2 3 (x² + 2) (3x-1) x 1 + 2 ) × ( 3 - 1 / 2 바 it 100 it ntos 0 Ja-10 it x- 4) False lim 97-) N 3 3 1 3 5) True " x = -) is an asymptote of Y - i ti It is vertical asymptote put Butt = 0 - x = - y_o is an asymptote for y= 1/2 (: as ao Tzo, horizontal asy tute) 7) True, y = 7 is an asymptote for y= 7x+1 6) Tere, 50-8 x to 9 l'as Y- It 72ti 5-8 it t 1 / xx 5-& 5