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f = m dal = m TABLOUE x"cm), A=x^(-0) B = x^(1=1) V2 What is "...",...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
2. Let if r and y are not both 0 f(x, y) = 0 if (x, y) = (0,0) (a) Show that and we both exist at the origin are are zero (b) Let v = (v1, v2) be a unit vector with vị and v2 both not zero. Prove that V (f) at the origin exists, and compute it directly from the definition. Does the formula Vu(f) = (Vf). ✓ hold at the origin? (c) Is f differentiable at...
Solve f, g, l, m x{n - 1] = 1.30. Determine if each of the following systems is invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output. (a) y(t) = x(t - 4) (b) y(t) = cos(x(t)] (c) y[n] = nx[n] (d) y(t) = x(t)dt ( x[n - 1], n>1 (e) y[n] = {0, n = 0 (f) y[n] = x[n]x[n – 1] ( x[n],...
A -11nC charge is located at (x, y) = (0.90cm , 0 cm). a) What is the x-component of the electric field at the position (x, y) = (5.2cm , 0 cm)? b) What is the y-component of the electric field at the position (x, y) = (5.2cm , 0 cm)? c) What is the y-component of the electric field at the position (x, y) = (5.2cm , 0 cm)? d) What is the y-component of the electric field at...
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What is F(-5)? (c) Compute the p.d.f of X. (d) Compute the mean of X (e) Compute the variance of X. (f) Compute the standard deviation of X (g) Compute the squared coefficient of variation of X.
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
Let f(x) = 2x4 +x4cos(1/x) for x ̸= 0 and f(0) = 0. Show that 0 is a global minimum x for f but for every neighbourhood V of 0 there exists x,y ∈ V such that f′(x) > 0 and f′(y) < 0.
Let f : [0, 1] x [0, 1] + R be defined by f(x, y) = {1 if y = 23, 0 if y + x2 Show that f is integrable on (0, 1] x [0, 1]. You may take the previous problem as given
Let f : [0, 1] x [0, 1] → R be defined by f(x,y) - 1 if y=%, 0 if y#x2 Show that f is integrable on [0,1] [0,1]. You may take the previous problem as given
1. Consider the region bounded by x = y, y = 0, and y=v2 - X. Sketch the region, and find its area.