Discuss the continuity of the functions f and g. (x, y) = (0, 0) (x, y) = (0, 0) (x, y) = (0, 0) (x, y) = (0, 0) O f is continuous everywhere except at (0, 0) and g is continuous everywhere. Of is continuous everywhere except at (0, 0) and g is continuous everywhere except at (0, 0). Of is continuous everywhere and g is continuous everywhere. O f is continuous everywhere and g is continuous everywhere except at (0, 0). f(x, y) = g(x, y) = x² 6,

Q: The set of functions {sin nx}, n = 1, 2, 3, ... , is %3D orthogonal on the interval [ -n, n]. Show…

A: Given- The set of functions sin nx, n = 1, 2, 3, ⋯, is orthogonal on the interval -π, π To Show-…

Q: (a) f(x) = F(x, 2): then ƒ'(x) = (b) f(x) = F(4,x): then f'(x) = (c) ƒ(x) = F(x,x): then ƒ'(x) = (d)…

A: Total derivative of function z = f(x, y) is given as dz=∂z∂xdx+∂z∂ydy We are allow to solve first 3…

Q: 2 cos (xy) 1-x-cosy 1. the point (0, 2) is in the domain of f. 2. the function is continuous at the…

A:

Q: Consider the set C = {(x, y) = R² | y² = x(1-x²)}. Is C a curve? If yes, why yes? If no, why not?

A: We shall plot the given curve y2=x6(1−x2).

Q: 12. The function f : [0, 2] → R is continuous on the interval [0, 1] and continuous on the interval…

A:

Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

A:

Q: f(x,y)=arcsin( x² +y² –1)+Jx² +y² -1 %3D

A: Definition set of the function is the interval in which the function is defined We know that Domain…

Q: Let f:[-1,1]-R be defined by f(x) =x²sin- if x is not zero and f(0) =0, then .A f is differentiable…

A: When a function is one–one, i.e., when the values of the domain are equal, the value of the range…

Q: Sketch a graph of a single continuous function with a y-intercept at ( 0 , 2 ) that has the…

A: Given, f(x) is a continuous function satisfying the following table.   -∞,-6 -6, 1 1, 3 3, ∞…

Q: If f is a function from X to Y and C, D are subsets of Y then A O f(C-D) =f(C)-f (D) B f'(Cn…

A:

Q: Find the domain and the derivative of the function f (x) = In x + V x² -25 Enter DNE in any empty…

A: The graph is shown below:

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

A:

Q: 1. Consider the function y = f(x) displayed below. y 3 это 5 (a) For which values of x in the open…

A: Let's analyze the function y = f(x) displayed in the graph and address each part of the question:(a)…

Q: X-|x Show that f,given by f(x) = (x ±0) is continiuos on R-{0}

A: f is continuous at a  If at x= a L.H.L = R.H.L = f(a)

Q: What is the range of the function f(x) = = x + b -, a, b = R and a, b =0? xa

A: range of fx=x+bx-a

Q: (-2,2), (0,1) (3.0), -5 -3 -2 3. 4. (-2,-1)/ (3.-1) -1 -2- Which statement is true ? A f(x) is not…

A: We know, a continuous function is a real valued function whose graph does not have any breaks or…

Q: lanarithmic differentiation bo find desivative of the function. (x+)"(x-s y= (x-3).

A:

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: 1 of f(z): is z2+2z+2 %3D

A:

Q: Consider the function f: R → R defined by f(x) = x³ – 3x + 2. Then (A) ƒ is increasing on the…

A:

Q: ((x+1)ª-y² Consider the function g(x, y) = {(x+1)4+y²' -1, if (x, y) # (-1,0) if (x, y) = (-1,0)…

A:

Q: Discuss the continuity of the functions f and g. Explain any differences

A: