57. Let |-x² _when x < 0 when x >0 f(x) = (a) Is f increasing? (b) Does f have an inverse? If so, what is it?

Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

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Q: What is the Range of f(X) = log X? None of these. (0, ∞) (- ∞, ∞) (3, 0)

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Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: 13. Find the end behavior for f(x) =x- 2 A. x- +0, f(x) - +o x--o, f(x) → - B. x +o, f(x) - +0 x--o,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: 250 4. Use second derivative test to determine the relative extrema of the function: f(x) = x2 +

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Q: 50. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Given: fx=3x-2 Concept Used: Linear function is continuous everywhere.

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: If f(x)= 8-cosh x/6+cosh x then f'(x)=

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Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x&lt;5x+1            ,  x≥5

Q: [1, 5] th- or f(x) is

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Q: Approximate to four decimal places f(x)=ex when x=-2.7183

A: Given function is f(x) = ex  Given that x = -2.7183

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

A:

Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

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Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: (9) F(<) = { —1, if - п <x<0 1, if 0sxп (h) f(x) — f -х, х, -1<x<0 0<x<1 if if

A:

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 102. Use the derivative to help explain why f(x) = x³ + ax increases for all x in (-*, *) when a 2 0…

A: Derivative of a function is determined by change of a variable with respect to change in another…

Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: True or False The cube root function is odd and is decreasing on the interval (-∞,∞).

A: we have to tell whether the given statement is True or False

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: 5. What is the definition of the derivative of a function f(x) ?

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Q: Show that x + is increasing on [1, 0).

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Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: 8- When f(x)-x' the value of error of Simpson's rule becomes .........

A: 8.) f(x)=x2f'(x)=2xf''(x)=2f'''(x)=0f(4)(x)=0

Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: Suppose that the function y=f(x) is increasing on the interval (-1,5). Over what interval is the…

A: The x-5 is offsetting the input of x. The beginning of the function increase is at x-5=-1 and the…

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: Show that x+1/x is increasing on [1,∞]

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

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Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

A:

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

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

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: x+4 if x2

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Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

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Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

A: Power Rule: The power for the derivative of the function xa is given by, The given function is f(x)…