Kumon Level N Test Study Guide Graded A+

18. Determine the values of the constants a and b that satisfy the following inequality. lim ax^2 +bx+5/x+3 = 3 {Ans: lim (ax+b+5/x)/(1+3/x)=3, lim (1+2/x)=1 a = 0 and b = 3}6. Obtain the 1st term and common ratio of a geometric sequence whose 5th term is 24 and 7th term is 96 First term: Common ratio: {Ans: ar^4=24, ar^6=96 1st term: 3/2 Common ratio: ±2}19. Draw the graph of the function defined by the following limit, and determine the continuity. f(x)= lim (x^n-1)/(x^n+1) {Ans: |x|<1, lim =-1 |x|>1, lim 1 x=1 lim 0 Discontinuous at x = ±1 and continuous everywhere else.}12. Evaluate the following limit when r>0 lim r^n+2/r^n + 1/r^n {Ans: lim (1+2*1/rn)/(1+1/r2n), lim r2n+2rn/r2n+1 r>1, limit 1 r=1, limit 3/2 07. Given a geometric sequence whose sum of the first 10 terms is 4, and whose sum of the terms from the 11th through 30th term is 48, obtain the sum of the terms from the 31st through the 60th term. {Ans: S10=a(r^10-1)/r-1=4 S30=a(r^30-1)/r-1=52 r^10=3, r^60= 1456 1404}11. lim 5^n + 2^n/3^2n +4^n = {Ans: (5/9)^n+(2/9)^n/1+(4/9)^n 0}