I need help finding the value of "c" that makes the functions continuous!!
f(x) = { (x^2 + x - 20) / (x-4).... if x does NOT = 4.
f(x) = { c ... if x = 4.
and then this set:
f(x) = { x+c .....if x is greater than or equal to 1.
f(x) = { 5 - cx^2 .... if x > 1
and: how do I explain why the equation: x^5 + 2x^3 + x +2 = 0 has to have a solution on the interval (-1,0)?
I need help finding the value of "c" that makes the functions continuous!! f(x) = {...
In the following exercises, find the value(s) of k that makes each function continuous over the given interval. 145. f(x) = $3x + 2, x<k 12x – 3, k < x < 8 3 153. Apply the IVT to determine whether 2* = x has a solution in one of the intervals [1.25, 1.375] or [1.375, 1.5]. Briefly explain your response for each interval. Determine whether each of the given statements is true. Justify your response with explanation or counterexample....
For what value of the constant c is the function f continuous on (-0, co)? cx2 + 5x if x = 6 f(x) = if x 2 6 x3 - cx Step 1 Note that f is continuous on (-0, 6) and (6, 0). For the function to be continuous on (-0, 0), we need to ensure that as x approaches 6, the left and right limits match. First we find the left limit. lim f(x) = lim (cx2 +...
Need help with functions. f(x) = V5-x -5 -4 -3 -2 -1 i 2 -2y=h(x) a) f(-4)= d) (h/g)(-2) = b) x so that h(x) = 4. e) f(g()) = c) 2h(4)-f(1)+8 (2) f) g(h(4)) =
I need help with my discrete math question. thanks in advance Let f(x) = 0 + 0,-1-1...+ar+ao with 00, 01,..., an being real numbers. Prove that f(0) E O(") by finding a pair of witnesses C and k such that f(x) < Cx" whenever I k.
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
C(10.1]) be the set of continuous functions f : lo. 11 → R 5) Let R from the interval [0, 1] to the real numbers. For any number ce [0, 1] (a) Show that the set R is a ring and that the set Ic is an ideal of R. (b) Is I UI2 and ideal? Is I, nI an ideal? C(10.1]) be the set of continuous functions f : lo. 11 → R 5) Let R from the interval...
Given functions f(1) = I 2-4 Find I+2 a) f(-x) b) f(x – 3) c) f(x +h) +4 d) f(3) e) is -2 excluded from th domain. Why. Explain.
5. (15') Define the inner-product on C([-1,1]), the space of all continuous functions on the interval [-1,1], by (f(a), g(x) = $ $(a)g(x) dr. (a) Use Gram-Schmidt algorithm to convert the set {1,1 + ,(1+x)?} to an orthogonal set. (b) Is the set you found in Part (a) still orthogonal if the interval of integral in the definition of inner-product is changed to [0, 1]? Explain your an answer.
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
3) Sketch the graph of the following rational functions. 2 a. f(x) = + +5r+6 x + 1 b. f(x) - 4x - 32 4) Solve each inequality. Give each solution in interval notation. a. + +8r+15 so b. 2x-5x > 3 C. (x - 1)(x+3)(x+5) > 0 x+3 d. > 0 x² - 5x+6 X +3 <2 2x+4 e.