(a) Find all values of a > 0 and BER such that the function cos(ax)-cos(x) for...
Consider the function S Ax? f(x) = - { x < 3 17 - Ax x3 Find a value of A so that the function is continuous at x = 3. - 12/17 17/12 12/17 17/3 - 17/12
Find the results of next functions 2.-Find the values of a and b such that fis differentiable at x 1 ax+b si 1s. Sol, a- 2, b-1. f(x)=1si x<1 x-7 si 0<x Sb| f(x) =16/x si x< 3 If ... a) decide a value of b far which f is continuous b)fis differentiable in the value of b that ycu find in part a)? 4.- In the following functions determine what is requested sen(x) si x < mx+b si x...
Find the constant a such that the function is continuous on the entire real line. f(x) = [ 5x2, x 21 ax - 5, x < 1 a =
Find all values x = a where the function is discontinuous. 3x - 5 if x < 0 f(x) = x2 + 5x -5 if x 20 O A. a = 0 OB. Nowhere O c. a = 5 OD. a = -5
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
2. Consider the linear equation Ax = b, AERmxn, beR. When m > n it is often the case that this equation is over-determined and no solution x exists. In this case we seek a “best” solution in the least squares sense. That is we solve minimize 3 || Ax – 6|| BERN Define f: RM → R by f(x) := 3 || Ax – b||2. (a) Show that f can be written as a quadratic function, that is, a...
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
6 ptsSuppose that f(x) = g(x? - 4x + 2), that is a continuous function, that g'(x) > 0 where I > -1, 9(1) < 0 where I < -1, and '(-1) = 0. On which interval(s) is the function increasing On which interval(s) is f decreasing?
12) Let f(A) = x + 1 xxo 0 x=0 (ax+ 2 x>0 a) Find lim f(x). X-70 b) Find lim F(x). X70 c) Find lim f(x). 13) Let f(x) = x - x .O 12.1 x 0 a) Find lim f(x). 6) Find
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +