What are all the values of y such that |−y|=8?
(a) | No such y exists. | |
(b) | 8 | |
(c) | 8 and −8 | |
(d) | −8 | |
(e) | 8, 0 and −8 |
If f(x)=x5+3,then f(x−h)=
(a) | (x5+3)−(h5+3) | |
(b) | (x−h)5+3 | |
(c) | x5+3−h | |
(d) | (x−h+3)5 | |
(e) | x5−h5+3 |
What are all the values of y such that |−y|=8? (a) No such y exists. (b)...
= (a) Suppose that limx+c f(x) L > 0. Prove that there exists a 8 >0 such that if 0 < \x – c < 8, then f(x) > 0. (b) Use Part (a) and the Heine-Borel Theorem to prove that if is continuous on [a, b] and f(x) > 0 for all x € [a,b], then there exists an e > 0 such that f(x) > e for all x E [a, b].
9+ 5 8 7 4 h(x) 6 3 y-values 5+ y-values 4 N 8(x) 3 2 1 3 2 X-values Ou 2 3 x-values If f(x) g() then h(x)' f'(4) = -13/2 Preview Get help: Video
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that: 1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
4. (a) Suppose that limz-c f(x) = L > 0. Prove that there exists a 8 >0 such that if 0 < 12 – c < 8, then f(x) > 0. (b) Use Part (a) and the Heine-Borel Theorem to prove that if is continuous on (a, b) and f(x) > 0 for all x € (a, b), then there exists an e > 0 such that f(x) > € for all x € [a, b].
2. Indicate a rectangle (that is, an interval of t-values and an interval of y-values) in which the requirements of the theorem on existence and uniqueness are satisfied for the non-linear initial value problem dy 1 sin(t)y(ty 2y +4t - 8) = 0 dt with the given initial condition. If no such rectangle exists, explain why not. Do NOT solve the equation y(5) 5 (b) (c) y(1)4 (a) y(0) 3 = = 2. Indicate a rectangle (that is, an interval...
e,f,g,h,i 1) Given: X 0xA4 and Y 0x95, a) Convert X and Y to 8-bit binary numbers. b) Compute the 8-bit sum X+Y of X and Y o) Compute Y the 8-bit two's complement of Y. d) Compute the 8-bit difference X"Y of X and Y. (Use two's complement addition.) o) Convert XiY, Y, and, X Y to hexadecimal. D What are the values of the condition flags z n c v upon computing X-+Y? g) What are the values...
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
number8 (6x²-1 xSl. a. DNE b. O c. 3 d. -3 e. 00 Given the piecewise function f(x) = { answer the questions belov Vx+ 24 x>1 76. Evaluate the lim f(x) if it exists. a. DNE b. 4 c. 5 d. 4 and 5 e. 25 7. State the domain of the function.a. (-00,00) b. (-00,1) C. (-0,1] d TX Given the function f(x) = 2x2 - 16x+1, answer the following questions (#8-#12) 8. Find the average rate of...
how do i solve this? For f(x, y), find all values of x and y such that f (x, y) = 0 and f (x, y) = 0 simultaneously. f(x, y) = In(4x² + 2y2 + 8)
Exercise 5. Extreme values (8 pts+12 pts) Let f(x,y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 mi b. d. 2) The point (1,2) is: a. a local maximum for f b. a local minimum for f c. a saddle point forf b. C.