Warm up 1. Do in notebook

Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda : warm-up Go over homework homework quiz Notes lesson 1.4

Notebook Table of content Page 1 Learning Target 1 1)1-1 A Preview of Calculus 2) 1-2 Finding limits graphically and numerically 3) 1-3 Evaluating limits analytically 4) 1-4 Continuity SectionHW AssignmentCompleted?Quiz Score 1.1 p.47: 4-6, p odd, all, all 1.3 p. 67; 37,39,47- 61,115,116,118, p. 68; 80-82, 89,90, p.79; 3-14,17-20, odd, Add: p 80; 87-90,95-98.

1-4 continue Intermediate Value Theorem In the middley- coordinate (IVT) If a function is continuous for all x [ a, b] and y is a value between f(a) and f(b) Then there exist an x= c between a + b in which f(c) = y.

If a function is continuous for all x [ a, b] and y is a value between f(a) and f(b) Then there exist an x= c between a + b in which f(c) = y. a b f(a) f(b) y c

EX: Show that f(c) = 5. f(x) is a polynomial therefore it is continuous By IVT there exist a x = c, For which f(c) = 5.

EX: Show that f(c) = 5. Find the c that is guaranteed by the theorem C = 1.311

EX 2: Show that f(c) = 0. f(x) is a polynomial therefore it is continuous By IVT there exist a x = c, For which f(c) = 0.

EX 2: What is the c? C =.596

EX 3(you try !): show that there is x =c such that g(c) = −1. Find the c guaranteed by the IVT.

EX 4:

A.P. Exam In doing these type of problems, always remember to explicitly write down that your function is continuous in the closed interval. Also remember to mention the name of the theorem you are using.

Example: The function is continuous on the closed interval [-2,2] Prove there are three zeros on the interval using the values in the table below and estimate the location of each. x-212 f(x)-414 Solution: Since f(-2) and f(-1) have opposite signs, 0 qualifies as a number between f(-2) and f(-1). Therefore, according to the intermediate value theorem, there is a number c, between -2 and -1 where f(c)=0. For the same reasoning, the sign changes between f(- 1) and f(1) and between f(1) and f(2) indicate that there must be a zero between -1 and 1, and between 1 and 2.

Use your calculator

Us the IVT to show that Has a root in the interval [0,2]. Show that f(c) = 0.

Extra Problems

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