6) Suppose that f(x) = x2 + 2 for -2 s x S 2. The range of the function is : a) O {y : 2 < y < 6} b)O {y : -2 < y < 2} c) O {y : 0 < y < 8} d) O All Positive numbers

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

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: Show that F = ху, , zy) is not conservative. 2

A:

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

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Q: 4. If f(x)dx = (x + 1)ln(|æ|) + C, what is f(x)? (To write absolute value, write abs(x). Do not…

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

A:

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,

A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: Let f(x, y) = 2x² + 3y2, then (2, 3) is not a critical point of f(x, y). Select one: True False

A: I have calculated the critical point of the given function

Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: 1 If f(x,y,z)= of then x-y-3-

A:

Q: Suppose f(x) = – 2x – cos r. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Show that the functionf (x ,y)=xy³onD: x|<2, ]y|<oodoes not satisfies Lipschitz condition.

A:

Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

A:

Q: Let f and g represent differentiable functions such that f ″ ≠ 0 and g″ ≠ 0.

A: Concavity of a function can be determined using the second derivative of the function. If the second…

Q: Let f(x) = x²+x+ 2 = Z₂ (x) prove that f(x) irreduciable Poly

A: The given function is  f(x)=x2+x+2.

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

A:

Q: If f(x) is continous on [a,b] then f(x) is differnitable on (a,b). True or False?

A: False Any differentiable function must be continuous at every point in its domain. The converse does…

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

A:

Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

A:

Q: let s(t)=3sin(2t)+5. find the absolute maximum and minimum of the function on the interval [0,2pi]

A: We have to find

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

A:

Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

A:

Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

A:

Q: show that F(X<1|Y<y) + P(X <1) for some z, y.

A: dependent events:  Two or more events are said to be dependent if occurrence of one affects the…

Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

A:

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

A: We can solve this using R.H.L ≠ R.H.L

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

A:

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

A:

Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: . If ∫f(x)dx=(x+1)ln(|x|)+C∫f(x)dx=(x+1)ln(|x|)+C, what is f(x)f(x)? (To write absolute value, write…

A: Definition used -  By differentiating the integral of a given function we can find the original…

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

A:

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

A:

Q: 2. Show by definition that the function f : R R, f(x) = ||, is continuous on R. Hint: you may need…

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Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].

A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…

Q: 4|x| – 3 pour x 1, x² – 4 f2(x) + V2 + x², || ||

A: Given that, f1x=4x-3x≤1-3xx2-4x&gt;1f2x=1+2+x2 To determine set of points which they are derivable…

Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

A:

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

A:

Q: 4 Suppose that f(x, y) = x* + y* – xy Then the minimum is 0

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…