Problem 3 Given the following graphs of f and g (both piecewise linear functions), define new...
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
Please solve this problem completely. (1) Length of graphs a) Let a path C be given by the graph of y - g(x), a b, with a piecewise C function g : [a,b] → R. Show that the path integral of a continuous function f : R2 → R over the path C is b) Let g: a bR be a piecewise Cl function. The length of the graph of g on (t, g(t)). Show that [a,b] is defined as...
2. The graphs of functions f and g are shown below. Circle your choice for each of the questions below. 1 3 2 g 0 2 a. Let u(x) = 160. Find the value of '(1) g(x) ii. 3 9 iv. / V. None of the above b. Let v(x) = x2. [f(x)]'. Find the value of v'(6). i. 1296 ii. -81 iii. 567 iv. 81 V. None of the above
Consider the sequence of functions fn : [0,1| R where each fn is defined to be the unique piecewise linear function with domain [0, 1] whose graph passes through the points (0,0) (, n), (j,0), and (1,0) (a) Sketch the graphs of fi, f2, and f3. (b) Computefn(x) dx. (Hint: Compute the area under the graph of any fn) (c) Find a function f : [0, 1] -> R such that fn -* f pointwise, i.e. the pointwise limit of...
Evaluate piecewise-defined functions Question Given the following piecewise function, evaluate /(-4). - 4x + 3 f(x) = x < 0 Osr<3 3S 2? + 2 Do not include "f(-4) =" in your answer. Provide your answer below:
O GRAPHS AND FUNCTIONS Inverse functions: Linear, discrete The one-to-one functions g and h are defined as follows. g={(-2, 5), (3, - 2), (6, 4), (8, 9)} h(x)= *+9 11 Find the following. 8'(-2) = 0 00 x X 5 ? (non ') (1) = 0
5 Consider the functions f and g whose graphs are given below. z y = f(x) -4 A3 -2 -1 1 2 3 4 y = 9(2) -4 -3 -2 -1 1 2 3 4 1 + f. Find (3) a. Find f'(-3). b. Find f'(1). g. Suppose p(x) = f(x)g(2). Find p'(-3). c. Find f'(3). h. Suppose q(z) = 5(). Find g(3). d. Find t'(-3). g(2) e. Find g'(1). i. Suppose r(x) = x2 f(x). Find r'(1).
UUTUVC vidps O GRAPHS AND FUNCTIONS Evaluating a piecewise-defined function Suppose that the function g is defined, for all real numbers, as follows. =x+2 if x = -2 g(x) = 3 if x = -2 Find g(-5), g(-2), and g(0). 8(-5) = 0 8(-2) = 0 x I ?
5.2. This problem (a) Find the piecewise linear interpolation function g(r) that fits these data. (b) Find the global interpolation polynomial p3(x) that fits these data concerns the data in Table 5.6. -1 0 1 2 0 1 0 1 y 5.2. This problem (a) Find the piecewise linear interpolation function g(r) that fits these data. (b) Find the global interpolation polynomial p3(x) that fits these data concerns the data in Table 5.6. -1 0 1 2 0 1 0...
3. Let f, g : [a,b] → R be functions such that f is integrable, g is continuous, and g(x) >0 for all r E [a, b] Since both f,g are bounded, let K >0 be such that lf(z)| K and g(x) K for all x E [a3] (a) Let n > 0 be given. Prove that there is a partition P of [a, b such that U (P. f) _ L(P./) < η and Mi(P4)-mi(P4) < η for all...