MATH117 Midterm: MATH117 Midterm 3 2014 Fall
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please write clearly and show enough work. Question 1. (5 pts) prove by " : f (x) := 2 x > 0 a =/ 0 but discontinuous at 0. 1 x 6 0 is continuous at every. Question 2. (5 pts) let f (x) :=( x + x2 sin 1. 0 x entiable everywhere on r and calculate f 0(x). x =/ 0 x = 0. Question 3. (5 pts) prove or disprove:pn=11 tan 1 the convergence/divergence of pn=11 1 na without justication) n2 converges. (you can use. Question 4. (5 pts) prove that there are exactly two solutions for the equa- tion x2 + 1 = 2 cos x. Question 5. (extra 2 pts) find a function f : r7! R such that f is dier- entiable everywhere, f 0(0) > 0, but there is no > 0 such that f is increasing on ( ; ).
