10) Determine the intervals of continuity. (a) f(x) = -3r² + 5x – 8 (b) f(x) = x2 – 9 V3-x (c) f(x) = || Vx+2

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 limit of f(x) = √(4 − x2) as x approaches −2 from the right.

A: We will find the limit by substitution

Q: 4. Given f"(x) 2x(x²-3) 2+1) find all intervals of concavity and x-values of any inflection points.

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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: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: Find the absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

Q: Find the absolute maximum and minimum values of f(x) = -(x² – x) 3 over the interval [-4, 3].

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: 1. f(x) = x² +x – 1 for all values of x -

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Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

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Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

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Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Find the absolute extreme of f(x)=x^3-12x on the closed interval [0,4]

A: for finding critical points take f'(x) = 0 then find the function value at the critical points and…

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

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Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: Use the first derivative test to determine the intervals where f(x) is increasing and decreasing and…

A: To find critical point put f'(x) = 0 If f'(x) &gt; 0 at each point in an interval I , then f(x) said…

Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: 4. Consider the function f(x) = (2x - 3)5. Discuss the continuity and %3D differentiability at x =…

A: 4.f(x) = (2x-3)15 from the graph, f(x) is not differentiable at x=32 , since slope changes at x=32…

Q: 2) State the intervals of concavity in the function f (x) = x3 + 2x2 – 4x + 5.

A: We have to determine the intervals for concavity of the function: fx=x3+2x2-4x+5 To check the…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: 21. Discuss the continuity of: for for 0sx 2

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A:

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

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Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Find the absolute maximum and minimum of f(x)=3x^3-x+1 on the interval [0,1]

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Q: 3. Determine the absolute maximum and absolute minimum on the interval [-1, 2] for the function…

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Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: 1 - X 0 3

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Q: Discuss the continuity of the function. x2 – 4 f(x) X + 2 f is discontinuous at x =

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Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: (1) Find and classify the extreme values of f(x) =6x* -4x over the interval [-2,2].

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 1) Find the absolute maximum and absolute minimum for f(x) = x-3x-2 on the closed interval [-2, 11.

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 7+6z – zº x 4 тх + b,

A: Given that,    A function is continuous everywhere means the function is continuous at every point…

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).→…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A:

Q: Find the absolute maximum and absolute minimum of f(x) =2x – 3x² – 36x + 2 on the interval [0,5]

A: Before finding absolute maximum and absolute minimum of any function over the given interval we need…

Q: Find the absolute maximum value of f(x) = x2 - 2x + 6 over the interval 0, 4

A: