1. True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. 1 (a) True or False: If f (x) → 0+, then f(x) 0o. (b) True or False: If f(x) → ∞*, then f(x) → 0+. (c) True or False: If a limit initially has an indeterminate form, then it can never be solved. (d) True or False: A limit “does not exist" if there is no real number that it approaches. (e) True or False: As limit forms, o² → o. (f) True or False: As limit forms, 2º → 00. (g) True or False: As limit forms, ∞ - 0 → 0. (h) True or False: The limit of a function f as x → c is always equal to the value f(c), provided that f(c) exists.

Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: 6. Determine, with reasons, the absolute maximum and absolute minimum of f(x) = x/2 – x on the…

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Q: 5) f(x) = x³ – x² + 1 B) Removable discontinuity at: x =-1 Essential discontinuity at: x = 1 A)…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x+5 interval [0, 3]. on the

A: The function is given by fx = x3-12x+5 To evaluate : The absolute maximum and the absolute minimum…

Q: 4) Find the critical points of the function f(x) = x²- 9 x* + 15x +3 and identify their nature. Draw…

A: Given that: f(x)=x3-9x2+15x+3 The graph is shown below

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

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Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

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Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

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Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: 1. Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) =…

A:

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

A:

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x +5 on the interval [0, 3].

A:

Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given: f(x) is a function continuous for every value of x whose first derivative is f'x=21-x1+x2 and…

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: 7. Consider the function *+1 if r< 2 f(x) = 3-1 if z 2 2 (a) Show that ƒ has no fixed point.

A:

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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Q: 2. Find the absolute maximum and minimum values of f(x)= x³ – 3x +1 over the interval [0, 3].

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Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: If f (x) = x(x - 2), then the critical points %3D of the function f(x) are

A:

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: 9. Given f'(2) does not exist and f"(2) > 0, is x = 2 a maximum, minimum, or neither of f? Explain.

A: Given: x=2f'(2) = does not existf"2&gt;0

Q: The interval where  f(x) = )=(√x+2) / x2 - 2x - 8 is continuous is ?

A:

Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: Find the absolute maximum and minimum values of f(x) = x – 2x on the closed interval [0, 2]. -

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: Find the local extrama of f(x)=x²-8x+12 on a closed interval [-2,5] O a. minimum value at x =4 is -4…

A: Topic- application of derivatives

Q: 7. Find the absolute maximum and minimum of f(x) = x!/² ( on the interval [0, 4]. %3D

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Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

A:

Q: 1. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 - 4 / x - 2 are…

A:

Q: The function ff has a continuous second derivative, and it satisfies f(1)=2f(1)=2, f′(1)=0f′(1)=0…

A: Given: f(1)=1, f'(1)=0, f'(1) = 2 A critical point of a function occurs when the first derivative…

Q: 84. Let f(x) = x' +3x² - 24x + 1 and g(x) =x' + 6x² - 36x + 1 . For what value(s) of x do both f(x)…

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Q: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

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

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) f'(x) > 6 for all x. = -2…

A: Given, fx is differentiable everywhere. f-4=-2 f'x≥6, for all x dydx≥6, for all x  dy≥6dx…

Q: 2 3 The absolute minimum of f(x)= 3 x³ - 2x 0n [-1,8] is y =

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Q: 5. Determine the critical points of the function: f (x) In(x² + 4x + 14) %3D Enter your answer

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Q: 26 a. The function f(x)=x- 6x² + 9x-3 is defined on the interval [0,5]. Find the critical points of…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: nd all the critical points of the function f(x)= ={ x² 23 if x<1 if x ≥ 1

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Q: 1 - X 0 3

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Q: 3/ Find the critical numbers of the function f(x)= x/5 (4-x)

A: The given function f(x)=x354-x

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: 3(a): Find the critical points of the function f(x) = 3x² – 6x. (b): Apply Rolle's theorem for the…

A:

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…