fx( )= L lim fx( )+ gx( )

... c [or the limit of f ( x ) as x approaches c from the left] is equal to ...

... c [or the limit of f ( x ) as x approaches c from the left] is equal to ...

February 27, 2015

... * Proof involves taking the double angle identities and solving for sin2u or cos2u. cos 2u = 1 - 2sin2 u ...

... * Proof involves taking the double angle identities and solving for sin2u or cos2u. cos 2u = 1 - 2sin2 u ...

Name: Date: 1.3 Guided Notes ~ Evaluating Limits Analytically

... 1) Use properties of limits to evaluate them analytically. A STRATEGY FOR FINDING LIMITS ...

... 1) Use properties of limits to evaluate them analytically. A STRATEGY FOR FINDING LIMITS ...

Slides 8

... Consider the Maclaurin series for f (x) and g(x) and let I be the intersection of the range of validity for both series. Then the Maclaurin series for f (x) + g(x), f (x)g(x) and f (g(x)) can be found using the Maclaurin series for f (x) and g(x). Example (Multiplication and composition of Maclaurin ...

... Consider the Maclaurin series for f (x) and g(x) and let I be the intersection of the range of validity for both series. Then the Maclaurin series for f (x) + g(x), f (x)g(x) and f (g(x)) can be found using the Maclaurin series for f (x) and g(x). Example (Multiplication and composition of Maclaurin ...

Chapter 1 Fourier Series

... |Sk (t) − f (t)| < for every k > N (, t)|. Then the finite sum trigonometric polynomial Sk (t) will approximate f (t) with an error < . However, in general N depends on the point t; we have to recompute it for each t. What we would prefer is uniform convergence. The Fourier series of f will conv ...

... |Sk (t) − f (t)| < for every k > N (, t)|. Then the finite sum trigonometric polynomial Sk (t) will approximate f (t) with an error < . However, in general N depends on the point t; we have to recompute it for each t. What we would prefer is uniform convergence. The Fourier series of f will conv ...

Introduction to Homogenization and Gamma

... (i) prove a compactness theorem which allows to obtain from each sequence (F"h ) a subsequence ;-converging to an abstract limit functional; (ii) prove an integral representation result, which allows us to write the limit functional as an integral; (iii) prove a representation formula for the limit ...

... (i) prove a compactness theorem which allows to obtain from each sequence (F"h ) a subsequence ;-converging to an abstract limit functional; (ii) prove an integral representation result, which allows us to write the limit functional as an integral; (iii) prove a representation formula for the limit ...

ABCalc_Ch1_Notepacket 15-16

... x 2 ax, x 2 For what value of a is the function f x continuous at x = -2? 2 x 2, x 2 ...

... x 2 ax, x 2 For what value of a is the function f x continuous at x = -2? 2 x 2, x 2 ...

3.4 Finite Limits at Points

... that the function is a fraction in which the numerator and denominator both approach zero as x approaches the limit point. This is one of many indeterminate forms; knowing we have 0/0 form tells us nothing about the value of the limit itself, or even if it exists. The reason is that a shrinking nume ...

... that the function is a fraction in which the numerator and denominator both approach zero as x approaches the limit point. This is one of many indeterminate forms; knowing we have 0/0 form tells us nothing about the value of the limit itself, or even if it exists. The reason is that a shrinking nume ...

Chapter 10: Logs and Exponential Functions

... We’ve differentiated y = 2x. What about y = ax in general? A similar argument to the above shows that the derivative of ax is a constant times ax. But don’t expect it to be the same constant. The constant will in fact be the slope of y= ax at x = 0. As “a” increases the graph of y = ax climbs more s ...

... We’ve differentiated y = 2x. What about y = ax in general? A similar argument to the above shows that the derivative of ax is a constant times ax. But don’t expect it to be the same constant. The constant will in fact be the slope of y= ax at x = 0. As “a” increases the graph of y = ax climbs more s ...