The domain of the function g(t) = vt – 5 is O R-{5} O R O (5, O [5, 0) о (-оо, —5) (5, 00)

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: The domain of the function h(t) = vt – 9 is O [9, 00) O R O (-00,9) O (9, 00) O (-∞0,9]|

A:

Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Let f(x,y) = x - 2xy – y“. Compute f(3,0) and f(3, – 7).

A: To compute f(3,-7) Given:- f(x,y)=x2-2xy-y2

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

A:

Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

A:

Q: hich z ∈ C the function e^(1/z) is holomorphic?

A:

Q: (b) Show that the u(x, t) can be written as u(x, t) = 0(x – at) + 4(x + at), where o and are…

A: The multivariable function u(x,t) is a rule that associates or fixes a number to a particular point…

Q: Find the MRSxy of the utility function U=In(x)+y.

A:

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Find the linearization L(x) of f (x) = tan x at a =

A:

Q: The domain of the function g(t) = vt – 8 is O (8, 00) O [8, 0) O (-∞, –8) O R O R-{8}

A:

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

A:

Q: Consider the function xy f(x, y) x²+xy+y² k if (x, y) = (0,0) if (x, y) = (0,0) State, with…

A: Given :  f(x, y) = xyx2+xy+y2if (x, y)≠(0, 0)kif (x, y) = (0, 0) To find : The value of k if it…

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Find the local linearization of f(x)=x^(2) at 2

A:

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A:

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x<0   So,…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

A:

Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

A:

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

A:

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Find (if any) the relationship between the empty functions u(x,y) = xcos(t²) – ysin(t²), v(x, y) =…

A:

Q: The domain of the function g(t) = vt – 6 is O R-{6} O R O [6, 0) O (6, 0) O (-∞, –6)

A: for the domain of g(t)  The term of square root should be non negative

Q: z - 3 z²(1 – 2²2) f(z) =

A:

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function -5x f(1) = | V1+ tª…

A: To differentiate the function by using first fundamental theorem of calculus f(x)=integration (x to…

Q: Show that f (a) = is Libschitz function on r+ 2

A:

Q: Prove that the function f(x) = cos x is strictly decreasing on the interval [0,1]. %3!

A: 5) Given that, fx=cosx

Q: Q3: a) Let f : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its -…

A: the function is invertible if its one -one and onto. The function is one - one if f(x1)=f(x2)…

Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

A:

Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: The domain of f(x) = Vx + 1 – V1 - x is O [-1, ∞) O (-∞, 1] O (-∞, –1] U [1, ∞) O [-1,1] None of the…

A: The given function is; f(x) = √(x+1) - √(1-x).

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: 2. Determine whether the following functions are linearly dependent or not by applying the…

A:

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Let f be the function from R to R with f (x) = x2. Is f invertible?

A: