[4 Pts. Use the definition of continuity to show that the function f is continuous at...
For what value of the constant c is the function f continuous on ( – 60,00)? f(x) Sca? + 6x if x <3 1 x3 cx if x > 3 C= Preview Question 9 Points norcihlo 1
[ 10 pts.] 9. Use the alternative limit definition of derivative to determine whether the function 8sinh(x/2) ifx<2 f(x)= is differentiable or not differentiable at 2x²+x-1 if x2 x=c=2 Show all work !!!
4. Show that lim -oxsin(1/2) = 0 by by appealing directly to the definition of limit. Recall that -1 < sin < 1. 5. Define a function that is nowhere continuous and another function that is continuous only at one point in its domain.
1. (2 points) Using the definition, find the Laplace Transform of the function: e21, 0<t<3 f(t) = 3<t
QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find Cand k such that f(x) < Cg(x) for all x > k. QUESTION 4 Finding the smallest number in a list of n elements would use an OU) algorithm.
1. Solve the following DE: (50 pts) (1, if 0<x51 a) y+ y = f(x), y(0) = 3 where f(x)= 0, if x>1 (10 pts)
(6 pts) Consider the joint density function f(x, y) = { (9- 2- y), 0<r<3, 3 Sy <6, 0, otherwise Find P(0 < < <1,4 <y<6).
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
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
2. Find the value of c so that the function is continuous everywhere. f(x) = 02 – 22 r<2 1+c => 2 {