MATH 410 Midterm: MATH410_BOYLE-M_FALL1996_0101_MID_EXAM_1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 410
• Professor: All

Document Summary

Each problem below is worth 20 points: (a) compute g (4), given g(x) = r (b) compute limx 0 [5x 3x]/[ln(1 + x)]. X t=1 ln(t2 + 1)dt: suppose f : r r is a di erentiable function whose graph is not a straight line. Prove that there exist numbers c and d such that f (c) is rational and f (d) is irrational: suppose a and b are real numbers such that 0 < a < b. A a: de ne a function f : r r by the rule f (x) = x3. Justify your answer: suppose f and g are functions from [a, b] r which agree except at nitely many inputs, and f is integrable.