To show that ( n + a ) b = θ ( n b ) ( n + a ) b = θ ( n b ) for any real constants a a and b b where b > 0 b >

Q: Let a, h, and k be arbitrary real numbers with a+0, and let f be the function given by the rule f(x)…

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Q: (e) If x and y are rational numbers, where y +0 and y # -1, then 1+ is also rational. 1

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Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: What are the values of a and b that make f(x)=ae^ax+bx^2+2b  x0 continuous and differentiable

A: Consider the condition for any function f(x) to be continuous at x = a. Use this condition at x = 0…

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: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: (a) Suppose that f is differentiable on R and has two roots.Show that f' has at least one root.(b)…

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Q: f'(2) for (x- x)(x² +2)(x² +x- 1) S(x) = %3D x + 2 O 676/5 O 379/7 O 587/3 O 384/9 O 585/4 O 699/7

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Q: if -1Sxくo -1くxくo xtl いーx if we suppose fx +2)=f(x) Vx find the fourie sum of the funchon and %3D

A: We will find fourier series for periodicity of given function and then will find coefficients .

Q: A fX-Y where X,Y e Z* , and 0s<X <23 and, 0<Y<59, X is hour of clock and Y is minute of digital…

A: Yes. f is well defined because we can measure the every numerical value of the function and can…

Q: The range of F (x) = 3 sin 2 x is -3≤F(x)≤3 -1≤F(x)≤1 -2≤F(x)≤2

A: The given function is: F(x)=3 sin(2x)

Q: For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions…

A: Given: The volume of rectangular box is: V=18 cm3 The rectangular box can be drawn roughly as:

Q: 7 Determine a value for r so that h(x) x + rx² – 7x has an inflection point at x = 5. 2 -- |

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Q: For all real numbers x, cos (2x)= (a) 2 sin x cos x2 sin x cos x (b) sin (x2)sin x2…

A: SOLUTION- formulaconsider the addition formulacos (A+B)=cos A cos B-sin A sin B

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: 4. Prove that if f(x) = aox" + a,x"-1+ ...+ an-1x = 0 has a positive root x = xo, then the equation…

A: Roll's theorem: If f is continuous function on [a, b], differentiable on (a, b) and f(a) = f(b) then…

Q: Let f(x) = { tan^−1 ⁡(2x) if x ≥ 0, ax+b if x < 0. For which values of a and b is f(x)…

A: topic- limits and derivatives

Q: 2. Consider a ball thrown in the air (f) defined by the formula f(x) = (3 + x)^2 whose domain is the…

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Q: What is the minimum value of F(x) = -4 sin

A: Answer and explanation is given below...

Q: f(6) = 2sece+ tan@ 6 <8<8| %3D 7. Find all critical numbers of of the function

A: We have to find critical numbers for given function:

Q: It is known that there is a rational number between any two distinct irrational numbers. Consider a…

A: Intuition: The given function somewhat looks like the following: This kind of function has a value…

Q: If f(x) <0 for all real numbers x then f is decreasing or increasing on its interval?

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Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

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Q: Find the area of the region enclosed by the curves  f (x)  =  4x + 15 and g(x)  =  2x + 33, and the…

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Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: 1) Find the absolute extremum values of f(x)=x2-4x+20f(x)%3DX2-4x+20 over the interval [1,4][1,4].

A: The extrema value of  function is f(4)=20

Q: What is the absolute extrema for (1-x) / (x^2+1) with [1,5]

A: We find the derivative of the given function using the quotient rule.

Q: 4. Evaluate (x - 1)(x + 1)da using the Fundamental Theorem of Calculus.

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Q: If f : [0, 3] → R is continuous not constant, then its range be a closed, bounded interval?

A: Yes true.

Q: prove that for any fixed x > 0. Fix a constant r>1. Using the Mean Value Theorem era > 1+rx

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Q: The derivative of f(x) = ax² will be greater than that of f(x) = ax, for a domain of (0,1), where…

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Q: For f(x)=(x^2+x−2)/(x+2) does the Mean Value Theorem apply on the interval [0, 2] and why?

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Q: Let f(x)={ tan-'(2x) ах+b if x20 if x<0 For which values of а and f(x) differentiable for every real…

A: Option second is correct, a=2 &amp; b can be anything.

Q: 2 Find the derivative of the algebraic function f(v)= v2- v+8 O 112+6v+2v² (v+8)2 O 112- 32v-2v²…

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Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: (7- 2n)(n+ 3) 1- 2n 3n* – 11n +9 V 9n + 4n + 1

A:

Q: On the interval 0 < x < 3, the function f (x) = x² – 8x + 16, which one it is  a) is concave down…

A: Given:      y=x2-8x+16 , 0 &lt; x &lt; 3

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

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

A: Given function is  fx=3x+4,   x≥4fx=Ax+B,  2&lt;x&lt;4fx=-2x+3,     x≤2where f has a limit at both…

Q: Given that f(x) = x + x2 for -π < x < π, find the Fourier expression of f(x).

A: Given f(x) = x+x2   -π ,π   — 1

Q: Find the critical numbers of the function f(1) = 2x – 3x² = 36z. Answer (separate by commas).…

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Q: I have no idea how to approach this question.  Any insight would be greatly appreciated.

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Q: Consider the function f(x) = 12x + 45x4 – 200x³ + 5. For this - function there are four important…

A: The given function is: fx=12x5+45x4-200x3+5 To find the critical points of this function, first,…

Q: Find the absolute maximum and minimum of the function f(x)=x^3-9x^2+15x+42 on the interval 0 is less…

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Q: Find the linearization at x = a. f(x) = a = 7 (Express numbers in exact form. Usc symbolic notation…

A: Linearization L(x) of the function f(x) at x=a can be written as below: L(x)=f(a)+f'(a)(x-a)

Q: B.Discuss the continuity of 1 x +- for x <0 y = -x3 for 0 < x < 1 -1 for 1 < x

A: The objective is to discuss the continuity of the given function.

Q: 50. If f'(x) = In(x²) and f(5) = 8, then f(3) %3D %3D

A: Given : f'x = lnx2f5 = 8

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: