Which of the following represents the domain of h(t)=−log(x)+3?   (2,∞) (−2,∞) (−∞,∞) (−∞,0) (0,∞)

Q: 5x +1 Prove that the function f: R – {3} –→R – {5} defined by f(x) is a bijection. x- 3

A: Consider the function f:R-3→R-5 defined by fx=5x+1x-3. To prove that f is a bijection, we have to…

Q: Find c such that the function 10 г c - || 26 х > с is continuous everywhere. c =

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Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: 3 -4 Define T: R2 → R by T(x) = Ax, where A = 4 -4 1 -1 -([-4]' T %3D 3

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: 10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you…

A: First we show that g(3)>4 ,so g(3) does not belongs to [3,4]So we can not say that g(x) is in…

Q: x*y"-xy'+y = 0 Y, = In x

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Q: Find the linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

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Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Let f(x,y) = x - 2xy – y“. Compute f(3,0) and f(3, – 7).

A: To compute f(3,-7) Given:- f(x,y)=x2-2xy-y2

Q: (@) Let FOR^ → R be a Function given by F(x₁, x,...,xn) = x²₁².. X²...x² x², where ) > x ²₁ =1. Show…

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Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

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Q: The function f is defined by f:R→ R/{-1} , f:x*-! x+1 **-1 and hf (x)= 2x – 3. (a) Find h(x). (b)…

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Q: The linearization at a = 0 to /3 + 9x is A + Bx. Compute A and B. A = B =

A: Given: f(x)=3+9x

Q: Find the Wronskian, W[x1, x2], of the following pair of functions. 1. x1(t) = t2 + 5t, x2(t) = t2 –…

A: We have to find the wronskian of given pair of functions.

Q: Use Fourier-Motzkin elimination to give a linear combination of the following in- equalities that…

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Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =>(x-1)(x+5) =>(x^2 +5x -x -5) =>(x^2 +4x-5)

Q: x*y"-xy'+y = 0 c) Y, = In x

A: Let's find.

Q: (Q4) Prove directly from the definition that the function f: R→ R defined by f(x) = 3r² +r for all r…

A: Sol

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: 요2s A) for F- 2K1-3y3+ K %3D prove That divc curl È)=0

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Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

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Q: 25. Suppose that T: R2 → R² is a linear operator such that T. -1 | T. -1 Is it possible to determine…

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Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: Find the linearization L(x) at x =a. .3 f(x)=4x² +3x-1 a =-3 L(x) =

A: The linearization of a differentiable function f at a point x=a is the linear function…

Q: Find the linearization L(æ) of y = (81+ 2æ²)-1/2 at a = 0. L(x) =|

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Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

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Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

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Q: If F = (x²)i + (2x²y)-(3-2)k find div f curl f at (1,-1, 1).

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5z+1 2. Prove that the function f : R – {2} → R – {5} defined by f (x) = is bijective. z-2

A: Consider the given information: The given function is, f:ℝ-{2}→ℝ-{5} f(x)=5x+1x-2 To show that f is…

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

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Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

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Q: The domain of f(x) = Vx + 1 – V1 - x is O [-1, ∞) O (-∞, 1] O (-∞, –1] U [1, ∞) O [-1,1] None of the…

A: The given function is; f(x) = √(x+1) - √(1-x).

Q: 4. Expand f (x) = 1 around a = 0, to get linear, quadratic and - 1-x cubic approximations.

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Q: QV A/ Find at (t-) as a funetion of t, if (x = t).(y= vE)

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Q: Find the Wronskian for the set of functions.{e−x, xe−x, (x + 3)e−x}

A: To Find theWronskianfor the set of functions. {e-x,xe-x,(x+3)e-x}

Q: Find the Wronskian for the set of functions.{x, x2, ex, e−x}

A: Given information: x, x2, ex, e-x The Wronskian is given by the following determinant.…

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y = x' on the interval 0 < x s 2. Write a…

A: Differentiate the expression of the slope with respect to x. For any value of x in the interval…

Q: Find the Wronskian for the set of functions.{1, x, x2, x3}

A: we have to find the wronskian for the set of functions. {1, x, x2, x3}

Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

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Q: y = In[(2x – 1)(x + 3)] with Respect to x by using the chain rule.

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Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}