MTH 161 Lecture Notes - Lecture 12: Intermediate Value Theorem, Squeeze Theorem

find the limit squeeze theorem (sin((n*pi)/6))/((n)^(1/3))

Find the derivative of the following function F(x)=∫ (2t–1)^3dt using the Fundamental Theorem of Calculus? Lower limit x^4 upper limit x^5

4. (26 pts) Evaluate the limit or say that the limit does not exist . If a limit does not exist, explain why. Show your work. You may NOT use a table of values, a graph, or L' Hospitals's Rule to justify your answer. (Note: Possible answers include + or -.) X-2 (a) (10 pts) lim – x+2 782 +5 - 3 (b) (8 pts) xvot COS X OSCILLATES lim x → x + 4 x2 Since -1 scos x si, we have that -1 (c) (8 pts) cos x x + 4 x2 1 x + 4 x? x + 4 x2 -1 1 and since lim – Elim- x+ x + 4 x2 + x + 4 x2 * +422=0, it follows by the Squeeze Theorem that lim Co2 = 0. X +0 x + 4 x 2