(10pts) 3. Use direct proof to show that if x and y are positive real numbers, then (x+y)" > " + y".
[9] Given any two real numbers x and y such that x < y, show that there exists a rational number q such that x < a <y.
Find the length of spiral curve T() = ----- 0 < > < 2”
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
Given z = 2 y2 – 3xy , find the slope of the surface at (1,1,-1) in the direction of ū =< 2,3>
Introduction to Analysis. Please write neatly so that I may understand your writing thanks. 4. (10 points) Prove that two real numbers a, b satisfy a<b for every e > 0, a <b+€
Prove or Disprove that: If a > 0 and b are two rational numbers, then a' is a rational number.
8. Consider ar? +5 I <3 f(0) = 12.c +b > 3 Determine a and b such that f is continuous and differentiable at x = 3. )={
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0