Q 11 If P(x) is a Cx where ci are constants. polynomial, show that limaP(x) = P(a). Hint: use the fact that P(x) =

Q: Q3) Find the Lagrange polynomial that fits the following set of four points and find the value of y…

A: Givenx0=-2, x1=3, x2=1, x3=7y0=5, y1=7, y2=11, y3=34

Q: Let f(t) = t³e6t + e - 2tsin 10 t. Find L

A: Introduction: The Laplace transform of the functions eattn and eatsinbt is given by…

Q: An epidemiological study of the spread of a certain influenza strain that hit a small school…

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Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D ...

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Q: Let f(x) = ax + bx . If (1,6) is a relative extremum point, then b is? %3D

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Q: x2 If F(x): is s an antiderivative of f (x), find / (-4f(x) - 2 Provide your answer below:

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Q: Find the local linearization of f(x) = x2 at 2. L>(x) = Submit answer

A: Ans.  =4x-4  For detail...go through the solution, I have done step by step

Q: Q/Use Lagrangian polynomial to find f'(2.1) from the following table x 1 2 3 17 22 f(x) 10

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Q: The linearization of f (x) = x² based at 3 is L (x) = [ Select ] [ Select ] (x - [ Select ] Done […

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Q: Find the linearization L(x) of the function at a. f(x) = x2/3, a = 27 L(x) =

A: The linearization of the function fx at x=a is Lx=fa+f'ax-a

Q: Suppase thut and such that (x?fH f'x) + 3x F(x) on and It exe If t i frowa Oh frow a

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Q: Let f(x, y) = ax²y + 3xy³ – 4x³ + axy. Find the value of a if fy(1, –1) = 13.

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Q: (b) Use the chain rule to show that if g is differentiable and g(x) # 0 then -d (æ) 9(x)?² %3D

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Q: Consider the function f(x)=/25–x². a. Find the linearization L(x) of f(x) at x = 3.

A: Given function , f(x) =25-x2Linearization of f/9x/0 at x=a is given by L(x) = f(a)+(x-a) f'(a)

Q: Vx + 4, i.e. Find the 2nd Maclaurin polynomial of the function f(x) f(x) = (x + 4)/2.

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Q: The function y x- + ax +E6 has zeros at x = -5 and x = 6. || Determine a and b exactly and enter…

A: If equation is cx^2+ax+b=0 than product of roots is =b/c Sum of roots=-a/c

Q: a³ f By definition, fray xxy dxdxðy Higher Verinetiues. True False

A: It is false.

Q: * Q1 In(x²-1) is: Vx²-2x The domain D, of the function f (x) = Df = (-00, –1) U (2, ∞) (A) D, =…

A: Solution:Givenf(x)=ln(x2-1)x2-2xFormula:ln ab= ln a+ln b(x-y)(x+y)=x2-y2

Q: Q8. Let f(x)= Ln(土) dt (6) Evaleata f'(10) = ? (b) Enlnts (Fツ (o)=? (f-)) (6) =?

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Q: Fird l the deivaie oLthe function. smpily nction. snpliy y= ln(seccx )) %D

A: To find the derivative of the given function

Q: (b) Given f(x)=9x – 6x² + x. Find F(x) dx in the form a In|g(x) + h(x)], where a is a constant

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Q: Q5: Find the least square polynomial approximation of the following data: 3. 9. 12 -4 -2 12 21 Hint:…

A: Using the Given hint we know y=a+bx+cx2  know we need to fit the function using Least square method…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D

A: Given f(x)=ax4+bx

Q: Find the linearization at x = a. f(x) = 9x', a = 1 (Use symbolic notation and fractions where…

A: Given that: f(x)=9x3 , a=1

Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: Consider the function f(æ) = 4x° + 4x7 – 6x? – 6. Enter the antiderivative of f(x) Preview

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Q: Q2: Let f(x) = 2x e-,x> 0 and Let Y = X2.Find G(y)and g(y). %3D

A: Implicit functions are the functions are not directly expressed, these are always expressed in terms…

Q: Given that "h(x) f(x) = r h(-1) = 5 h'(-1) 8 Calculate f'(– 1). Hint: Use the product rule and t

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Q: An epidemiological study of the spread of a certain influenza strain that hit a small school…

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Q: Find a and b so that the function 2x3 – 7x2 + 4, x -2 is both continuous and differentiable. a = b…

A: Function and its derivative mist be continuous so check the continuity at x= -2

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table x 1 2 3 |f(x) 10 17 22

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Q: Let (a,b) be the critical point on a polynomial function y=f(x) and b±0. Which of the following is…

A: Given, a, b be the critical point on a polynomial function y=fx  and b ≠0 We have to find the true…

Q: Q3/a) what is the half range expansion of F(t)=t? 0st<1

A: A Fourier series defined on the interval or or is called a half range Fourier series. Here the…

Q: Syppose that Ts Cx) centered at a for f(x) is giver by T5 (x) = 3+5(x-2) +8(x-a)?+a(x-2)+ (x-2)5.…

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Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

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Q: Use the EVT to find the maximum and minimum values of the function f(x, y) = e4x²-5 y on the disc x²…

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

Q: ☺ using the definition f'sx) = li fCxth)-fx) find f'(x) when fex) %3D 2x-3

A: The given function,    f(x)=72x-3

Q: Let F (x) = In tdt then F'(x) = et3 6xe – 3x'e 3xe* – 3x'e

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Q: Find the linearization L(x) of the function at a. f(x) = –9x?, a = -9 L(x) =||

A: Given:- The function is, f(x)=-9x2 To find: - The linearization L(x) of the given function at a=-9

Q: Find the value of c guranteed by the Intermediate Value Theorem ( explain why is is guranteed).

A: Given:

Q: 3x Let F (x) = In tdt then F'(x) = 9xe - 3xe 6xex - 3x e 3xe - 3x°e 9xe* - 3x'e

A: We use Leibnitz Theorem.

Q: An epidemiological study of the spread of a certain influenza strain that hit a small school…

A:

Q: By first fundamental theorem of Calculus if f (x) = V19 +t²dt then f'(3) is? %3D

A: Given f(x)=∫0x219+t2dt

Q: Find the linearization L(x) of f(x) at x = a. 3 36) f(x) = x, a = 27

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Q: 4 For what value(s) of x is the function f(x) 2x2- 6x | NOT continuous? A. x=0 andx= 3 B. x = 3 only…

A: We need to find points at which f(x)=42x2-6x is not continous.

Q: Use the grapn of g(x) below to answer what follows 4 3 2 - 2 -it'23 4 5 4 1-

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Q: Find a and b so that the function 7x3 – 3x? + 8, x -2 f(x) = ax + b, is both continuous and…

A: To Determine: find a and b if f(x) is both continuous and differentiable. Given: we have…

Q: QB3) Verify fxy-fyx for the function f (x, y) = 4x (Iny) + 4y (Inx) + (²²4 2²

A: We have to prove fxy=fyx for the given function.

Q: + 7x° – 8x³ – 4. Consider the function f(x) = 8x° An antiderivative of f(x) is F(x) = Ax" + Bx" +…

A: topic - integration