Name: Date: 1.3 Guided Notes ~ Evaluating Limits Analytically
... Attempt to evaluate the limit by direct substitution. (Remember this will only work if the function is continuous when x = c.) If the limit of f(x) as x approaches c CANNOT be evaluated by direct substitution try to find a function that agrees with f for all x values other than x = c. In other words ...
... Attempt to evaluate the limit by direct substitution. (Remember this will only work if the function is continuous when x = c.) If the limit of f(x) as x approaches c CANNOT be evaluated by direct substitution try to find a function that agrees with f for all x values other than x = c. In other words ...
Applications of Differentiation
... p had 4 or more roots, say a < b < c < d. Then p0 would (a, b), (b, c), and (c, d) so p0 would have at least 3 roots. ...
... p had 4 or more roots, say a < b < c < d. Then p0 would (a, b), (b, c), and (c, d) so p0 would have at least 3 roots. ...
Improper Integrals
... in terms of areas. Since both functions are positive, the integrals simply represent the are of the region below their graph. Let Af be the area of the region below the graph of f . Use a similar notation for Ag . If 0 ≤ g (x) ≤ f (x), then Ag ≤ Af . Part 1 of the theorem is simply saying that if Af ...
... in terms of areas. Since both functions are positive, the integrals simply represent the are of the region below their graph. Let Af be the area of the region below the graph of f . Use a similar notation for Ag . If 0 ≤ g (x) ≤ f (x), then Ag ≤ Af . Part 1 of the theorem is simply saying that if Af ...
LINEAR APPROXIMATION, LIMITS, AND L`HOPITAL`S RULE v.03
... Let's consider the linear approximation to y = x - 1 at x = 5to understand what we mean by the error. The linear approximation is y = ÅÅÅÅ1 x + ÅÅÅÅ3 . We want to know when we can use the linear approximation and being accurate in our calculation within ...
... Let's consider the linear approximation to y = x - 1 at x = 5to understand what we mean by the error. The linear approximation is y = ÅÅÅÅ1 x + ÅÅÅÅ3 . We want to know when we can use the linear approximation and being accurate in our calculation within ...
REVIEW FOR FINAL EXAM April 08, 2014 • Final Exam Review Session:
... n=1 approach a unique number L as n increase, that is, if an can be made arbitrarily close to L by taking n sufficiently large, then we say that the sequence {an } converges to L, denoted by lim an = L. If the terms of the sequence do not approach a single number as n increases, n→∞ ...
... n=1 approach a unique number L as n increase, that is, if an can be made arbitrarily close to L by taking n sufficiently large, then we say that the sequence {an } converges to L, denoted by lim an = L. If the terms of the sequence do not approach a single number as n increases, n→∞ ...
