3. The function f(x) = 5 is continuous at all points of its domain? x²-16 A. True C. Maybe B. False D. Neither

Q: For a < b real numbers, let ƒ : [a; b] × [a; b] → R be such that (1) for each y € [a, b], the…

A: As per the question for a &lt; b real numbers, we have  f : [a; b] × [a; b] → ℝ , such that : for…

Q: inverse of the function x= 2/ y-3

A: Given:

Q: x – 8/€ composition of two functions_ 5 /8 — х Write the function h(x) as a

A: A function whose input is another function is a composite function. The function h(x)=8-x3/5 if to…

Q: dh + 2h = 0 dr

A: Given:rdhdr+2h=0

Q: (2.xy + 16x + 4y + 32) dx + (3xy – 9y – 7x + 21) dy = 0, y (4) = – 7

A:

Q: Continuity of multivariate functions

A: Here we will find the limit of the function.

Q: Homogeneous function

A:

Q: ach function, state whether it is Function 1 {(-2,-4),(0,-5),(2,-8),(4,-12)} Linear

A:

Q: Fill in the equation for this function. 2 UN -π/2 TT/2 4 TT 3m/2 f(x) = [ ? ]cos(x − −˜_ ) + π

A:

Q: y²x = 1 + Cy

A:

Q: Use Green's function to solve: y" – 4y' + 3y = ex, y(0) = 1, y'(0) = %3D

A: Introduction: Green's function is another method to solve an initial value problem. Green's function…

Q: X'0, X1,* , Xn E (a, b) are arbitrary points such that x; # x; for i # j. Fur- thermore, let P be a…

A:

Q: A table for f(x) is shown below X f(x) -2 -1 0 1 2 -4 1 20 -3 A table for h(r) is shown below X 1 2…

A:

Q: 9. e' cos (x) =1+ sin (xy) 10. tan (x – y) = 1+ x2

A: Given the equations 1)ey cos(x)=1+sin(xy)2) tan(x-y)=y1+x2We need to find implicit differentiation…

Q: Linear functions and their graphs Determine the function representedby the line in Figure 1.19.

A:

Q: Assume that f: [0, ∞) → R is a continuous function such that lim ƒ(x) = ∞. x48 a) Prove that f…

A: Given that  is a continuous function such that .(a)We need to prove that  attain its minimum value…

Q: piecewise function

A:

Q: 19. Derive the formula for the Product Rule for four functions. (fghw)' = f'ghw+ fg'hw+ fgh' w +…

A:

Q: Problem 4 Consider the nonlinear system i2 = 3x7r2 a) Confirm that xı = x2 = 0 is an equilibrium. b)…

A: Given non-linear system is x1˙=-x1x22x2˙=3x12x2

Q: 8) gla) = -4a - 3 fla) = a² - 5 Find (gof)(1) %3D

A: Given,           ga=-4a-3 , fa=a2-5

Q: x = C1cos0 + C2sin0

A:

Q: Exercise 0.4. Assume that g : R → R is a periodic continuous function. Prove that f(x) = 2x + g(x)…

A: Continuity and uniform continuity are two different things. A continuous function may not be…

Q: Problem 1. Let (X, dx), (Y, dy) be metric spaces, and equip R with its usual absolute value-metric.…

A: Given: Let us consider the given,X,dX,Y,dY a) Let us determine the sequence of functions fn:ℝ→ℝ b)…

Q: e. The function 8(m)=100e10m m=minutes, and g(m)3Dgrams after m minutes. Use the function to give…

A: