7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x < 2 f(x) = Br? + 2 for 2 3

Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

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Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

A: f(x)=x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: 20 10 If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

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Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for r 2

A: Please see the the answer below.

Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x&gt;3 we have to check the given function is…

Q: 11. For what values of "a" and b is the function is continuous at.x31 f(x) = ( 3ax +b: x>1 %3D 11:…

A: A function f(x) will be continuous at a point a if:   limx→a-f(x) = f(a) = limx→a+f(x)

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: Let f(x)=4+ln(x2+3)f(x)=4+ln(x2+3) be a function defined on the interval [0,∞)[0,∞). Find the…

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Q: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

A:

Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

A:

Q: What is the critical number c and function value f(c) of f(x) = (x – 2)² + 3x – 3. If necessary,…

A:

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

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Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

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Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

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Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x&gt;3 now show that it is continuous at x=3 or not.…

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

A:

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

A:

Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

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Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 – 3x on…

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Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: 4. `s.] Find the number a and b at which f is continuous everywhere? x² -1 if x 2

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Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: x², if xs1 4. Let f(x) = . Find f. (1) andf'(1). Does f'(1) exists? 2x, if x>1 Show that the…

A: 4. fx=x2,if x≤12x,if x&gt;15. y=f(x)=x2-3x

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

A: