The following function is defined for D = [-3, 3). f(t) = -0.13 +0.2ť+0.3t + 3...
For the following piecewise-defined function f. find the critical numbers, local extreme values, and absolute extreme values on the closed interval 6, 90 20r109 if 6<214 f(z) 14< <18 8 87 if 18 < z<90 10+237 if Critical number(s) Preview Local minimum value(s) Preview Local maximum value(s) Preview Absolute minimum value: Preview Absolute maximum valug: Preview Points possible: 1 This is attempt 1 of 2. Submit For the following piecewise-defined function f. find the critical numbers, local extreme values, and...
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
Q8*. (15 marks) The following f(t) is a periodic function of period 2π defined over the domain when 0 < t < t π f (t) When π Express f(t) as a Fourier series expansion
Q8*. (15 marks) The following f(t) is a periodic function of period 2π defined over the domain when 0
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) = t for 0 <t < 1; f(t) = 4 for t > 1. (a) Determine the function F(x) = $* f(t) dt. (b) Sketch F. Where is F continuous? (c) Where is F differentiable? Calculate F' at the points of differentiability.
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on its domain?
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on...
Let f(t) be a function on [0,00). The Laplace transform of fis the function F defined by the integral F(s)= si e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. 4 0<t<2 f(t)= 3, 2<t -8 The Laplace transform of f(t) is F(s) for all positive si and F(s)=2+ otherwise.
3. (28 points) Let f(x,y) = 2x3 - 6xy+3y- be a function defined on xy-plane. (a) (6 pnts) Find first and second partial derivatives of f. (b) (10 pnts ) Determine the local extreme points of f (max., min., saddle points) if there is any. (C) (12 pnts) Find the maximum and minimum values of f over the closed region bounded by the lines y = -x, y = 1 and y=r
a. Find f( 5), f(-3), and f(8) b. Sketch the graph of the piecewise-defined function. xif xs0 f(x) 1 if x>0 c. Determine the domain of f d. Determine the range of f. X f(- 5) %3D а. (Simplify your answer. Type an integer or a fraction.) f( -3) = (Simplify your answer. Type an integer or a fraction.) f(8) = (Simplify your answer. Type an integer or a fraction.) b. Choose the graph of f(x). O A. В. C....
Let it) be a function on (0.co). The Laplace transform of is the function F defined by the integral F(6)= c-stat)at. Use this definition to determine the Laplace transform of the following function. 21. 0<t<3 f(t) = 4. The Laplace transform of it) is F(s) for all positive and F(e)=3+26-6 otherwise, (Type exact answers.)
Also :
FS (2.8)
FS (4)
FS (5)
The function f(t) is defined by -3t+6, 0<t<4 f(t) = -3, 4 < t < 5. Let f (t) denote the periodic extension of f(t), with period 5. Evaluate f (-2.3), f (O), f (7.5), f (9.2) and state the value to which the Fourier series of f (t), FS(t), converges for each of the following values: t = 0,t = 2.8, t = 4, t = 5. Enter all your answers...