Find the domain and the range For fo llowing Functions. A)F(エ, ): 32ーy 3) F cey) コ-ュナリ C) F (x^ Y): 125-4*-y2 S) FLx,)ジm ょーツ)

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: Show that f(2) =

A: We will show that derivative does not exist using definition. Then we will use geometry.  Calculate…

Q: Show that the function f defined by (r, y) = (0,0) f(x, y) = { 22 + y (r, y) # (0,0) x + y

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Q: Suppose that | f(z)dz = 2, | f(z)dz = 1, %3D [ 9(2)dz = - 5, | 9(2)dz - 2. Then, | (=) – g(2))dz =

A: Given: ∫25fxdx =2, ∫23fxdx =1, ∫25gxdx =-5, ∫23gxdx =-2 To evaluate:∫35fx-gxdx We know that…

Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

Q: 3. Where is f(x) = concave up? Justify your answver. %3D

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 1, Use the definition of error function, prove that (주)나

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Q: Find the length of f(r) = on the interval [1, 2]. Show all calculations. %3D

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Q: To plot the function f(x) == %3D 2x over [0,5], we use fplot('exp^(-x) /2*x'[0,5)…

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: Let f(r) 3 sec(5z) %3D f'(x) =

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: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

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Q: Show that if f (x, y, z) = 0 then = -1.

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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: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: Point X is equidistant from F and T. Furthermore, point Y is equidistantfrom F and T. Does that mean…

A: To check: Whether the point X and Y are equally distance from F. Given: The point X is equidistance…

Q: Use the linear approximation of the function f(x)=sqrt(9-x) at a=0 to approximate the number…

A: We know that the linear approximation of f at a is L(x)=f(a)+f'(a)(x-a). Here, f(x)=9-x and a = 0.…

Q: se the product rule to evaluate f(x)g(x)| at x =

A: Given that: f(x)=2x3-8g(2)=5g'(2)=-3

Q: Find and sketch the domain of f(r, y) In(r - y) 6. -

A: Given:      f(x,y)=lnx-y9-x2-y2·x2+y2-4    Interval notation : -3,0∪0,3   Set builder notation:…

Q: Calculate the largest vertical distance between f(x) = (x + 4)² and g(x) of [- 1.66, 9.66]. 2x2 over…

A: The vertical distance between the curves is given by: (x+4)2-2x2=x2+8x+16-2x2=-x2+8x+16 We have to…

Q: find and sketch the domain of the function f(x,y)= Suqare root 2x-y

A: f(x,y)=2x-yAs we know that domain refer to set of positive values  while range is the set of…

Q: Use f- calculate to (f!) in the damain of f= ==-1, %3D

A: Given: f-1(x)=1x-1 ;          14≤x≤1

Q: Let f(x) = /90 – x and g(x) Then the domain of fogis equal to a, b for = x? r. %3D - - and %3D

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: (1, if x 2

A: Using the given piece wise function, we can plot it in given intervals.

Q: If f(x) = 2sin-'(u) where u =L, then: f'(x) = %3D f (2) =

A:

Q: Show two ways to differentiate ƒ(x) =

A: The function f(x)=1x10. We have to differentiate this function.

Q: Determine the concavity of f (x) = x* 6x2 12 x + 2. O a. concave downward (-o, 3) and concave upward…

A: Given,           The function is fx=x3-6x2-12x+2.To find: The concavity of the function.We know…

Q: proove that if  f(x,y) is differeniable at (a,b), then f(x,y)is continous at (a,b).

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Suppose Hx isa one-to-ens tunctien auch that f-3)-5. Which of the following tacts must be trar?

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Q: Find the largest open interval where the function is changing requested. as 9) Increasing y = (x2 –…

A:

Q: Consider the function f(x) = x³ – 3x2 – 9x + 4 At what interval is the function concave upward? -…

A: The function is given by fx = x3-3x2-9x+4 To evaluate: The interval on which the function is concave…

Q: Find the averuge valuc of the function fcx)-4x4 on the interval [2,6],

A: Given : fx = 4x4

Q: Let f(æ) = Vr² – 5, g(x) = , h(x) = go((gof)+h(x)) at x=-1? Find - %3D 22-9

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Q: Does the Mean Value Theorem apply to f(x) = |x – 7| on the interval [1, 9]? Explain.

A: No

Q: find the value of c that make the function continuous

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Q: 5, what is f'(x)?

A:

Q: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

Q: f. Is the domain of f(x,y) = In (3x2 + 3y²) bounded or unbounded? Bounded Unbounded

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Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: (-3,3) Homework f(x) G5,1), Evauate (4,-2) -- ,f(x)dx

A:

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: By using formula of lenght of sub tangent and sub-normal

Q: Determine where f(x): V4 - x2 is continuous. Express the answer in interval notation.

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Q: Can the Mean Value Theorem be applied to the function f(x) = 1/x2 on the interval [−2, 1]? Explain

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Q: 4. Determine the number of zeros of the function f(2) = 2zª – 2iz³ + z² + 2iz – 1 - in the upper…

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Q: If f(x)=x', find f'(x), f"(x), f'''(x). (Pls 2. use the definition method)

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Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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