Express /4(x) in terms of Jo(x) and J;(x). [#Hint: use identity D]

Q: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

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Q: If f (x) = Vsin¬1 (2x²) , then f' (x) = (sin¯"(2z²))*-/1–4z“ True False

A:

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

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Q: Discuss the continuity of f(x) = 2x + 3 at x = −4.

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Q: Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂…

A: 1.   0 ∈ ∅ As ∅ is empty set so it can't contain any element. Hence 0 can belongs to ∅. Answer:…

Q: Show that the functi on When x g 0 f(x)= +1 0 . When x = 0 is discontinuous at x = 0.

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Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: Find Valume x zO; Ekort the X3D2; 0 about the x- axis

A:

Q: 4. Use the Fundamental Theorem of Calculus to evaluate [(-3) -

A: The objective is to find the integral using fundamental theorm.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4e* on the interval [0,…

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Q: 5. Differentiate using quotient rule: x+2 y x-2

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Q: Show that f (x) = 7 x - 4 is invertible and find its inverse .

A: f(x)=7x-4 is a linear function. So for one value of x , there is one value of f(x) This means f(x)…

Q: find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

A: Derivative of function

Q: State the theorem for general Version of the Chain Rule.

A: The chain rule of derivative is used to find the derivative of composite functions. The chain rule…

Q: (√t-9) dt

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Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

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Q: Write the formula of partial derivation with respect to x?

A: Partial derivatives  Let  f(x,y) is a function given , in which f(x,y) partially depends on x and y,…

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

A:

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

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

A: Lx = f(a)+f'(a)(x-a)

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: What are the zeros of f(x) = 2 cos (3x) + 1 on the interval [0, π]?

A: The zeroes of a function f(x) are the values for which f(x) becomes zero. We know that, cosx=cosθ if…

Q: Draw the y = sinx and y = 1- x² on the domain -2 <x<2 and filling the between the funtions.

A: the filling part is given below-

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: Coo show that the f(x,y)=X+4xy-3y gdegrad is homogenaow of

A: Concept used: The function is homogeneous of degree n if fkx,ky=knfx,y. Given: fx,y=x3+xy2-3y3…

Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: for x 1 x -1 = ( JI- 2 for x = 1, show that flx) is continuous at x = 1

A: If fx=x2-1x-1  for x≠12  for x=1then to show that fx is continuous at x=1.

Q: Find a point c satisfying the conclusion of the MVT for the function У(х) 3D 16/х on the interval…

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Gven that Pe3 -3 3 f On Compore

A: 3. Given that, P=52337-1, Q=5-31237. (i) Obtain the value of PQ as follows.…

Q: Differentiate the following f(x) =/20x- sin²(2x) Ox –

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Q: Show that 2Vx < e* for all real numbers x.

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Q: Let f(x) = – 3 sin( – 2x – 5) – 6?

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Q: EER(F}}

A: Introduction - F-test of H0:β1=0consider the hypothesis test H0:β1=0Hα:β1≠0Note that Yi^=b0+b1Xiand…

Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Use f (x) = -2 In(x + 1) to do the following: %3D

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Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: ) Show that |2x - 2|-|x+1| +2≥0 for every x € R.

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Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: 2 (1 – :-) d.x

A: Given ∫141-2x2dx

Q: Find fqix(q|x) for x € {0,1} and all q.

A: Given Information: Q be the continuous random variable with pdf, fQ (q) =6q(1-q)       ; 0≤q≤10…

Q: (*;)-()0)

A:

Q: 2 Vtan 0 de

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Q: Show that cosh x> 1 + x² for all x.

A: comparison

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: