([x] + 2 Classify the discontinuity of fat x = 0 and at x= 1 given that f(x) = {x-|x-2| if x < 0 if x > 0 x2-1

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: Find the absolute maximum and minimum, if either exists, for the function below on the given…

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Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

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: 4) Find the absolute maximum and absolute minimum values of f on the given interval. (a)f(x) = 3x² –…

A: Find the absolute maximum and absolute minimum values of fa) f(x)=3x2-12x+5 , 0,3 b) fx=x-lnx , 12,2…

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3].

A:

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

A:

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: 3. Given f(x) = x³ + x² – x + 1, on the interval bsolute maximum and minimum values, and indicate…

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Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: 2) Consider the function g(x) = x³ + 3x2 - 9x + 2 on the interval [-4,2]. Find all local extrema,…

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Q: 4. At x = 4, the function f(x): (x², x ≤ 4₁ = is (4x, x>4 A. continuous but not differentiable B.…

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Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: Find all critical values for f(æ) = (x – 4)°(æ – 5)*. %3D - The critical values occur at X = commas)

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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,…

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Q: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

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

A:

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

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

A:

Q: For the following function: a - find all critical numbers b - find the open intervals over which the…

A:

Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

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Q: x+4 Which will prove that f(x) = %3D x2+16 is continuous at C= -4? 1. f(-4)=0 II. lim f(x)=0 III.…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

A:

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Concept: L'Hospital rule:Let f and  g be functions that are differentiable on an open interval (a,b)…

Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

A:

Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

Q: For f'(x) = (x – 7)(x + 1)(x + 5), Find (i). What are critical points of function (ii). On which…

A: Given,            f'(x) = (x - 7) (x + 1) (x + 5)

Q: 4x-8 i- -2 x +3a

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 15 over the interval [1,3].

A: To find the extreme values of the given function f(x) = x2 - 3x + 15 over [1, 3]

Q: x² -2, x#-2 2. f(x)= 4,x=-2 a. Removable discontinuity at x = 1; Essential discontinuity at x = 1 b.…

A:

Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

A: Given,  fx = x2-4x+9    We have to find the absolute extremum values in the interval 1, 4

Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

A:

Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

A:

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: limx→∞lnx3x=limx→∞3lnx2·1x1    By using L'Hospital's rule=limx→∞3lnx2x=limx→∞3·2lnx·1x1    By using…

Q: 4. At x = 4, the function f(x) = (x², x ≤ 4 (4x, x>4 A. continuous but not differentiable B.…

A:

Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Consider the limits:

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

A:

Q: g. The function f(x) = e- is continuous on the whole real line. %3D p(x) h. If f(x) is a rational…

A: g. Given,     The function fx=e-x is continuous on the whole real line.     True, the exponential…

Q: f(x+h)-f(x) For f(x) = V3x + 13, find f '(x) using the definition f '(x) = lim f'(x) = Using this,…

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8