[PDF] x 1 Given x) = Find lim f x) numerically x 1 x 1

Rolle’s Theorem – f c f - UTEP MATHEMATICS

f fx () f x

1 1 fx x = + The Maclaurin series for f is given by 11,−+ − + +− +xx x x36 9 3LL()n n which converges to f ()x for 1 1 −<

Example 2 f x) = x n where n = 1 2 3 - MIT OpenCourseWare

x+ n(Δ )(n−1 O(Δ 2 −x = nx n −1+O(Δx) Δx Δx Δx As it turns out, we can simplify the quotient by canceling a Δx in all of the terms in the numerator When we divide a term that contains Δx2 by Δx, the Δx2 becomes Δx and so our O(Δx2) becomes O(Δx) When we take the limit as x approaches 0 we get: lim Δy = nxn −1 Δx→0 Δx

x 1 Given x) = Find lim f x) numerically x 1 x 1

1 x2 B lim x→2− x+2 x−2 C lim x→1+ 1 x−1 D lim x→0+ 1 x E lim x→3+ x √ x2 −9 F lim x→1 1 (x−1)2 The population P, in thousands, of a small city is given by P(t) = 10+ 50t 2t2 +9 where t is the time in years What is the rate of change of the population at t = 2 yr? Round your answer to the third decimal place 5 A-1 557

41 Applications of the First Derivative

4 1 Applications of the First Derivative Objectives: 1 Given a graph, determine the intervals of increasing, decreasing, or constant 2 Use the derivative to find where the function is increasing or decreasing

The Algebra of Functions - Alamo Colleges District

The Algebra of Functions Like terms, functions may be combined by addition, subtraction, multiplication or division Example 1 Given f ( x ) = 2x + 1 and g ( x ) = x2 + 2x – 1 find ( f + g ) ( x ) and

LECTURE 8: Continuous random variables and probability

fx(x) dx Px(x) > 0 LPx(x) -1 ,x fx(x) > O J: (x)dx 1 Defin tion: A random variable is co t1nuous f - ca be escr· ed by a 1p F

1 Definition and Properties of the Exp Function

4 1 Arbitrary Powers Arbitrary Powers: f(x) = xr Definition 13 For z irrational, we define xz = ez lnx, x > 0 Properties (r and s real numbers) • For x > 0, xr = er lnx • xr+s = xr ·xs, xr−s = xr xs, xrs = (xr)s • d dx xr = rxr−1, ⇒ Z xr dx = xr+1 r +1 +C, for r 6= −1 Example 14 d dx x2 +1 3x = d dx e3xln(x2+1) = e3xln(x2

Random Variables and Probability Distributions

) k 1, 2, (1) It is convenient to introduce the probability function, also referred to as probability distribution, given by P(X x) f(x) (2) For x x k, this reduces to (1) while for other values of x, f(x) 0 In general, f(x) is a probability function if 1 f(x) 0 2 where the sum in 2 is taken over all possible values of x a x f(x) 1 34