(b) Show that xE R, x2 - 4x + 5 > 0.

Q: 1 Find Vf if f = 2 /x²+y² +z?

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Q: What is derivation of f(x) = (2x² – x + 1)³ at %3D Xo = 1 ?

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Q: Which is equal to (x) given that g(x) = 1- 3x and h(x) = V?

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Q: What value of a makes ƒ(x) = x2 + (a/x)have a point of inflection at x = 1?

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Q: The domain off(x) = 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, ∞)

A: Domain: The domain of a function is the set of all input values for which the function is defined.…

Q: (b) Let f(x)=√x and g(x) = 2x+5, find: (1)fog(x) (2)gof(x)

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Q: Let f(æ) = (2x² + 1)(3z + 5). %3D The sum of the coefficients of f'(x) is equal to

A: Find derivative and sum of coefficient.

Q: Veridy that the approximate root of xa2 is: 1+Xn- Xn 2

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Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

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Q: Q No. 2 Discuss the differentiability of ƒ(x) = (x – 3)' at x = 3 by using definition and…

A: the given function is: f(x)=x-323 we have to discuss the differentiability of the given function at…

Q: Use the intermediate value theorem to show that the equation x + 2x + 1 = 0 has a solution in the…

A:

Q: find the critical point and classify it. a. f (x,y) =xlny + x2 -4x -5y + 8

A: The answer is given below:

Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: 6. Find the domain of y = Vx+ 4x + 5x + 2 + Jxl-|x+1]

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Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Use Horner's method to find po=2, Q(2) where f(x)= x³-2x2-5

A: the given polynomial is f(x)=x3-2x2-5 rewrite in standard form f(x)=x3-2x2+0x-5 to find the quotient…

Q: 5. y = xArctanx - In v1+x

A:

Q: Sketch the crach oF I (x) = 3x² +7x-6 x²+4x+1 F I(x)

A: GivenF(x)=3x2+7x-6x2+4x+1

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Find the linear approximation of f(x) = x4 + 3x2 at a = 1.

A: We first find f'(a)=f'(1) f(x)=x4+3x2f'(x)=4x3+6xf'(1)=4(1)3+6(1)f'(1)=4+6=10   We now find f(1).…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

A:

Q: The real part of sech (2-j3) is -3.7245 -3.5906 O 0.0403 O -0.0106 -0.5309 1.0357

A: The Euler's formula is widely used formula in complex analysis. It makes a bridge between the…

Q: Find the convolution of (a) Ila * IIa. (b) f(x) * f(x), where f(x) = e-l=l, -0 < x < o. %3D

A: Convolution : The convolution of two functions f(x) and g(x) is given by f(x)*g(x)=∫-∞∞f(y)g(x-y)dy…

Q: In(1 – a²) V4 – x² – y? Find and sketch the domain of f(x) = %3D

A: The domain of the function f(x) is the values of x for which the function attains the real values.…

Q: 3- Show that the function y = x3 + 3x + 3 satisfy the y" + xy" 2y 0

A: Function does not satisfy the given inequality. See the attachment

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: (b), f(x) = In (x² – 4)

A: Since you are asking only for b. Here is your answer.

Q: 2- Show that: 2 J1(x) = (-1)m x2m+ (2m + 1)! m=0

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Q: Express the follo lowest form +4 a 2 1-3x S+x

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Q: y = x2 - 2x over the interval (0, 2]:

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Q: Sketch the natural domain of f (x, y) = V(2x² +2y² – 8.

A: The find the domain of a radical function, f(x,y)=2x2+2y2-8, the radicand must be nonnegative,…

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

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Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

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Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: y = v1 - x2 from a = 0 to r = ;

A:

Q: (B) Solve f(x) = x³ – 2x – 5 using Secant Method, correct up to 3 decimal places. Where xo=2 and x1=…

A: Given that fx=x3-2x-5  also x0=2 and x1=3 solve it using secant method

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: Differentiate with respect to t 100 = x2 + y2

A: give equation ;- 100=X2+Y2 when we differentiate above equation with respect to t , we get

Q: 1 d.x x/1+ x6

A: LetI=∫1x1+x6dxPut1+x6=u                         (1)squaring on both side1+x6=u2x6=u2-1…

Q: The derivative of f(x) 4 (22 +17x) is O -4c (2a + 17) O -4r 2(2x + 17) O 4x + 68 O 4x 2(2x + 17) O 4

A: Here, it is given that f(x)=4x(x2+17x) We need to find the derivative of the function f(x).

Q: How do I figure out where the discontinuity can be removed in this equation: F (u)= u-4/u1/2-2 when…

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Q: 16. Use f(x) = 2x and g(x) = to evaluate the exp %3D a. (fo g)(2) b. (g o f)(- 7)

A: We will evaluate the given expressions.

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: In(x² + y² – 9) V25 – x2 – y? - Sketch the domain of f(x, y) -

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & Z then simplify.

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: If x &lt; 0 and y &gt; 0, determine the sign of the realnumber. xy

A: Let x&lt;0 and y&gt;0