71. Find the value of a that makes the following function differentiable for all x-values. fax, x? — Зх, ах, if x < 0 g(x) if x > 0

Q: 4. Consider the function f(x) = |x + 1|whose graph is shown below. 4. a. Is the function…

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Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: Determine the value for k that will make the function continuous at c = 4. x² – 9 if x 4

A: Left-handed limit of a function at a point is obtained by approaching the point from the left on the…

Q: Determine the value of the constant a for which the function f(x) is continuous at -4. x + 7x + 12 x…

A: Given function is fx=x2+7x+12x+4 if x≠-4a                  if x=-4 We have to find the value of a.…

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f\x). If f(0)= 22 and f(0)=5, then…

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Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: 3) Verify Rolle's Theorem for the function f(x) = [-4, 4]. Justify your answer. 5x + 6 defined over…

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

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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: 9. If a continuous, differentiable function f has values f(-2) = 3 and f(4) = 1, what can you say…

A: Give that: f(-2) = 3 and f(4) = 1

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: 4x -5x-6 for x +2 Given f(x) 2-V2x 4 for x = 2 Is the function f continuous at x = 2 ? Give…

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

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: For what value of the constant c is the function f continuous on (-0, 00)? C =

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Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

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Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: 4. Explain what it means for a function f to be continuous at a point x = c, with a sentence that…

A: Given: We have to explain about function f  to be continuous at a point x=c

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

Q: For what value of the constant k is the function f continuous on (-∞, 0)? 5x2 – kx + 7 if x 7 k =

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Q: Sketch a function that has all of the following characteristics: * infinite discontinuity at x = −2…

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Q: For what value of the constants A and B is the function f continuous on (-∞, ∞)? A√x+6-1 for x 3

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Q: 10 if x c - everywhere then: С —

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Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

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Q: What type of discontinuity occurs at x = 1 for the piecewise function? if x <1 if 1<x 3+ x h(x) =…

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Q: 8. If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given that if a continuous, differentiable function f is equal to 2 atx=3 and at x=5, Our Aim is to…

Q: For what value of the constant c is the function ƒ continuous on (-∞, ∞)? cx² + 2x if x 2.

A: We know :- Limit definition at x=a  ⇒limx→a-f(x) =limx→a+f(x)  if function continous at x=a then…

Q: True or false: Suppose f(x) is a function that is differentiable everywhere. If f'(x) < 0 for all x,…

A: We have to choose true or false

Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f(x). If f(1)= 5 and f'(1)=10, then…

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Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: 6. True or False The graph of the function f(x) = x? is increasing on the interval (0, ). (

A: f(x)=x2

Q: 3. Find the value of eachvariable.

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Q: 14х y = Зх-6

A: Given:   To determine: excluded x value for the function.

Q: IV. Determine whether the function is continuous at the indicated number. Sx² – 1 (x +5 x < 3 if 14.…

A: Function is continuous at a given point if it satisfies following conditions at that point:- 1)…

Q: The first two sub-intervals in the table are [0, 0.5] and [0.5, 1.0]. When calculating L6, we should…

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Q: For what values of a and b wou la the function f be continuous at every 'humber x'? real ax + 26 if…

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Q: For what value of the constant c is the function f continuous on (-∞, 0)? if x 5 C = Need Help?…

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Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 + 8x + 15…

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Q: What are the discontinuity and zero of the function f(x) = x^2+8x+7/x+1    Discontinuity at (1,…

A: Given,        fx=x2+8x+7x+1        fx=x+7x+1x+1      Discontinuity at x=1  at f1=x+7=8…

Q: Find the value of a and b that will make the function continuous. for x 1/2

A: The function f(x)=1x,        for x&lt;-1ax+b,  for  -1≤x≤121x,         for x&gt;12. We have to find…

Q: 4. Determine the possible pairs of values (a, b) which make the function below continuous…

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Q: Over which interval is the function f (x) = x3 -4x2 + 5x concave upward?

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Q: x+4 if x2

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Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

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Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: 26) The interval where f(x) is decreasing is?

A: Answer and explanation is given below...

Q: If |ƒ(w) - ƒ(x)| &lt;=|w - x| for all values w and x and ƒ is a differentiable function, show that…

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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: 1 3 In y = In (5x + 7) - - In (x + 9) + In C 3

A: The equation is given by 3ln(y) = 12ln(5x+7)-13ln(x+9)+ln(C) To determine : The expression for y as…

Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

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