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# Calculus 1 Test 2 Study Guide CLA MAT 191.006

Mercer

GPA 3.0

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## Popular in Mathematics (M)

This 1 page Study Guide was uploaded by Delanie Fancher on Tuesday February 2, 2016. The Study Guide belongs to CLA MAT 191.006 at Mercer University taught by Yuanting Lu in Winter 2016. Since its upload, it has received 34 views. For similar materials see Calculus I in Mathematics (M) at Mercer University.

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Date Created: 02/02/16

3 Spring 2016 MAT 191.027/028: Topics for Test 3 Monday, April 4th, 2016 1. (Section 2.10) Linear approximation. Using the tangent line at x = a to approximate a function near x = a. 0 f(x)= f(a)+ f (a)(x a) 2. (Section 3.2) Mean Value Theorem. • Find the c that meets the conclusion of the Mean Value Theorem. f(b) f(a) f (c)= b a • Application of Mean Value Theorem. 0 – If f (x)=0forall x, then f(x)siacnan. – If f (x)= g (x)forl x, then f(x)= g(x)+ constant. (We can use this result to prove identities. Review worksheet problems.) 3. (Section 3.5) Understand limits involves inﬁnity. For example, 2 2 2 2 x 3x + x 1 3 x x x!1 x +1 =0 , x!1m 2x 4x +3 = 2 , x!2 x 2 = 1, x!2m+ x 2 = 1 4. Curve Sketching. • Find the critical numbers. (f (x)=0or f (x) DNE.) • Determine the interval(s) where a function is increasing/decreasing.(Sign chart for f (x).) • Find the x-values for candidates of inﬂection points. (f (x)=0or f (x) DNE.) 00 • Determine the interval(s) where a function is concave up/down.(Sign chart for f (x)). • Additional information for curve sketching. – Find all the relative minimum/maximum (y-values). – Find the x-value(s) where the curve crosses the x-axis. – Find the y-value where the curve crosses the y-axis. – Check if the fuction has any vertical/horizontal asymptotes. 5. Optimization. Be able to set up optimization problems by • Similar triangles • The Pythagorean Theorem • The distance formula (which really is just the Pythagorean Theorem) • Formulas for area, volume and surface area • Cost.

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