1. For each of the following relations, indicate whether it is a function. If it is a function, give its range. If it is not a function, explain why. f:R → R such that f(x) = Vx а. b. f:R → R such that f(x) = Vx²

Q: If y = f(x) is a function that has a removable discontinuity at x = e and a, b, c, d e R - {0}, then…

A:

Q: Use the limit definition for the derivative to calculate f'(x) for each of the following if f'()…

A: we have to find the derivative of f(x)

Q: Let f be defined as follows: Sx+5 for x> 5, f(x) = Зах for x <5 } For what value of a is the…

A: A function f is continuous at a if limx→af(x)=f(a).

Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: Consider the piecewise-defined function f defined by 8 -3x2 11 6x { if x 1 if x 1 f(x) Find f'(1).…

A: Given,

Q: The relation f = {(x, y) E R X R Ə is 1. Not function 2. Function 3. On to function 4. One to one…

A: Given :  f(x) = x/x+1

Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: Are the following functions quasiconcave, quasiconvex, both, or neither: f(x) = x³ - 2x f(x₁, x₂) =…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Suppose that f(x) is a differentiable function such that f'(4)=5 and f(4)=4. If g(x)=xf(x), then…

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Q: Let f be the function defined as follows. y = f(x) = V9x + 1

A: Given y=f(x)=9x+1

Q: Use the limit definition for the derivative to calculate f'(x) for each of the following if f'(x)…

A:

Q: Suppose f:R-IR is a diffeetiable function which satısfies flo) = 0 We wart to show f': IR → IR is a…

A: Given that f:ℝ→ℝ is a differentiable function which satisfies f0=0. It is required to show that f' :…

Q: Which of the following statements must be true for a function that is concave up everywhere?

A: Which of the  following must be there for a function than is  concave up everywhere .

Q: Suppose f is a continuous function where f(7) = 9 and f'(7) = 6 . The tangent line to the graph of y…

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Q: Consider the following function: - 4 if x 3 Find the values of a and b that make f continuous…

A: The function is continuous every where, if it is continuous at each point in the domain. The…

Q: f(x,y) = -x4 +2x2y - 1/2y2-4y +12

A: To find the relative extrema of the following function.

Q: Suppose f(x) and f'(x) have the following values. -7 -6 -5 -4 -3 4 -9 1 9 2 6 x f(x) -2 f'(x) 1 -2 3…

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Q: 1. Determine whether the following functions are continuous at the given point. a) f(x) = 1 ; а — 3…

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Q: 1) Sketch the graph of a function with the following conditions: V D = {x € R\x # 0,4, 5} f(x) 0…

A: We have condition at function.D = {x∈R|x≠0,4,5}f(x)&lt;0, When x∈(-2,0)∪(2,4)f(x)&gt;0, When…

Q: . Suppose that f(r) is a function given by for 0<r<7, f(z) = for -n <I<0.

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Q: For what value of the constant c is the function f continuous on (-, o)? cx2 + 8x if x 3 C =

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Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

Q: Suppose that a continuous function g satisfies: | g(x)dr = 24 and 9(2x)da = 21. 0. .2 Find

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Q: Please explain how to solve. Thank you

A: Let's find.

Q: For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how…

A: First, we find limx→3g(x). We rewrite g(x) as, g(x)=(x-3)(x-1)(x-3) If x≠3 we have…

Q: Which of the following statements is false for a function f that can be differentiated at least…

A: We have to define which statement is wrong

Q: Determine whether the following function is continuous at the given point z- 3z+ 14z -5 f(2) 3z -1…

A: A function fx is continuous at x=a if limx→a-f(x) = limx→a+f(x) = f(a)  Given: fx=3x2+14x-53x-1…

Q: 22. For the following functions, identify any points of discontinuity, and if any exist, classify…

A: We will identify points of discontinuity of f(x) and g(x) and classify each points of discontinuity…

Q: 14. Consider the following function: if - 10 SIS0 3. h(r) = {15x - 3| if 0<<4 2r +1 if r24 What is…

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Q: Consider the following. if x s 2 S2 - x |x² – 4x + 4 f(x) = if x > 2 Is f differentiable at 2? O Yes…

A: The given function is f(x)=2-xif x≤2x2-4x+4if x&gt;2 to find the given function f(x) is…

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then…

A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

Q: If we apply Rolle's Theorem to the function f(x) = 2x- 16x 6 on the interval [2, 6|, how many values…

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Q: 3. The peicewise function, f(x), pictured to the right consists of segements of linear functions.…

A: We have to determine which statement are true.

Q: Suppose that f(x) is differentiable function such that f' (1)=8 and f (1)=4. If    g(x) = (f(x)) /…

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Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)=0. If g(x)=sin(f(x)), then…

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Q: Determine whether the following function is continuous at the given point z =: 3x2 + 14x – 5 1 3…

A: Given. The function fx=3x2+14x-53x-1  x≠13163x=13 We have to check the continuity of the function at…

Q: Which of the following is the domain set of the function f(x.y)= arccos(x² + y² - 3)+In(x² +y² -3) ?

A: In this question, we evaluate the domain of multivariable function and in second part we check the…

Q: Aen vity # 2 BLs auss ME! t) flx):1 Xスー 2.

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Q: determine whether or not the IVT applies to show that the given function takes on all values between…

A: The given function is

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=2. If g(x)=xf(x), then…

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Q: Are there any values of r for which the function A is discontinuous? Why?

A: We have to find out

Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

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Q: Determine whether the following function is continuous at the given point z= 22 +9z – 5 f(=) = 2x-1…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 8x - 1 on the interval [0, 4], how many…

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Q: Suppose that f(x) is a differentiable function such that f'(4)=6 and f(4)=4. If g(x)=xf(x), then…

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Q: "hich of the statements a through k about the function y = f(x) graphed here are true, and which are…

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Q: (i) Let ƒ be the function defined on (-o, 0) by f(x) = r$(3 – x)}. (2 – x) -2 Given that f'(x) = and…

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Q: Determine where the following functions are discontinuous, if anywhere. 0 x = 0 f(x, y): otherwise…

A: We need to find continuity of given function.

Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

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Q: On what domain is the function f(x) = 5+ V2x + 6 continuous? %3D

A: Let's find.