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Differentiation Critical points MA4001Engineering Mathematics 1 Lecture 14 Derivatives of Trigonometric Functions Critical Points Dr. Sarah Mitchell Autumn2014 Differentiation Critical points Animportant limit To calculate the limits of basic trigonometric functions we need to know the limit lim sinx. x→0 x Fromthegraphit looks like the limit might be 1 (if the function is continuous). Differentiation Critical points lim sinx x→0 x Asthefunction is even the two one-sided limits must be the same,sowejustneedtocheck lim sinx. x→0+ x ...
Name__________________________ AP Calculus BC Summer Review Packet (Limits & Derivatives) Limits 1. Answer the following questions using the graph of ƒ(x) given below. (a) Find ƒ(0) (b) Find ƒ(3) (c) Find (d) Find lim fx( ) lim fx( ) x5 x0 (e) Find (f) Find lim fx( ) lim fx( ) x3 x3 (g) List all x-values for which ƒ(x) has a removable discontinuity. Explain what section(s) of the definition of continuity is (are) violated ...
Partial Differentiation for functions of more than one variable: f=f(x, y, ) Take area as an example A=xy For an increase xx in , A=yx y constant 1 For an increase yy in , A=xy x constant 2 For a simultaneous increase x x A= xx+ y+y−xy ()() A y 2 =yx+xy+xy AA 12 =xy++xy A=xy xy A y 1 In the limits →xy0, →0 ∂∂AA →A dA= dx+ dy ∂∂xy y x ...
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