Exercises 35–42: Write the given expression in the form f(x) = a(x – h)² + k. Identify the vertex. 35. f(x) = x² - 3x 36. f(x) = x² – 7x + 5 37. f(x) = 2x² – 5x + 3 38. flx) = 3x² + 6x + 2 39. f(x) = 2x² – &x – 1 40. f(x) = --² - x 41. f(x) = 2 – 6x – 3x 42. f(x) = 6 + 5x – 10x?

Q: Rewrite c(x) = (x ^ 2 + 5x + 2)/(x - 3) in the form y = q(x) + (r(x))/(b(x)) has degree less than b.

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Q: Suppose that y= 2(1- e *). Compute y' and show that y' =2-y. y' =] 2-y%3D Does y' = 2-y? O Yes O No

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Q: Let flx)-4x H2 %3D

A: Topic = Function

Q: 2 / x + x ^ 3) ^ 16 any constant term?

A: We use binomial expansion.

Q: 20. Solve for the Wronskian of the set of functions: 3x - 1, x* - 2. 2x + 3 A. 4x (9x + 10x-90x -…

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

Q: Q2) Evaluate va (do your calculations for particular a ) a)By using Fixed point iteration method, i)…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Show A-B graphically and calculate A-B algebraically?

A: The difference of u→-v→ as a sum u→ + (-v→).                                u→ = -5,2  v→ = 6,-5…

Q: Axk + 2xk + k +1 = xk+1 + xk + k +1 = 0. cion to the last equation is %3D

A: Given, let the function f be equal to△yk2; therefore, equation (6.52) becomes…

Q: 54, find r such that the m 5a. A -[ 3 -3 -2

A: A matrix 'A' is equal to its own inverse when  A2=I where I is the identity matrix.

Q: If f(x) = 3x — 7, find the image of 2 and the preimage of 2

A: Given: fx=3x-7 To determine: Image & pre-image of 2.

Q: 6 2, find the following. - V (gof)(x) 2√2(1-2x) X (b) the domain of (gof)(x) in interval notation −…

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Q: Gues ALGEBRAI PRACTICE/ SECTION 1/ 40F 9 In the following table, indicate which of the relationships…

A: Verify the features in the relationships J and K. 1. A distance of 5 units between its x-intercepts.…

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: Find the sixth term of the G.P. 6, 2,..

A: Given first two terms of a geometric progression series,  6,2,... To find the sixth term of the…

Q: 4. Let X € R"xm. Show that x™x >0.

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Q: Prove that the equation 3x² – 3x + 2 = 0 has a solution on interval [0; 1].

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Q: 9. Find the general solutions of X' = AX with A =

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Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: Eliminate the arbitrary constants from the following equations. x2 = axy + by

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Q: Find the linearization at x = a. f(x) = 9x*, a = 1 %3D (Use symbolic notation and fractions where…

A: We have to find the linearization of the given function.

Q: 7) What is the minimum value? h(x) = x2 + 4x - 7 %3D

A: Given:- h(x)=x2+4x-7  To find:- minimum value of h(x)

Q: then the ² u - y² is მყ2

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Q: Test the equation for symmetry. y = x3 + 10x

A: Given equation:                         y = x3+10x

Q: find the value of ( ƒ ∘ g)' at the given value of x. ƒ(u) = 2u/u2 + 1, u = g(x) = 10x2 + x + 1, x =…

A: Since f(u) is not clear. Considering two cases to solve the problem:

Q: The graohg of the funcation f(x)=ax^2+bx+c has vertex at (1,4) and passes(-1,-8). Find a,b, and c

A: Given equation f(x)=ax²+bx+c has vertex at (1,4) and also passes through (-1,-8) To find a,b and c

Q: Find the linearization at x = a. y = (10 + x)-1/2, a = 9 (Use symbolic notation and fractions where…

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Q: Given that y= (2e - 6x +5) , show that y-

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Q: Prove that ax² bx C + + (x − a) (x −b) (x −c) (x-b) (x-c) x-c -+1 x³ 3 (x-a)(x-b)(x-c)

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Q: Determine the values of b and c if f(x)=÷x* 1 x²+bx +c has vertex 3 ,6 5

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Q: Find the linearization at x = a. f(x) = 3x², a = 1 (Use symbolic notation and fractions where…

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Q: Suppose that X is a (A = e-100, p = 3e-100)-BCP. %3D What is P(X(1)X (2)X(3) = 4)?

A: Correct answer is 4.

Q: Discuss the maximum and minimum of x?+y'+6x+12.

A: Given: x2+y2+6x+12

Q: 3 13. Evaluate x2 Vx + 2 da -1

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Q: Find the 3rd term of (x + 2)³.

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Q: a51 - Find ax2@y3 if f(x,y)-x.e z

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Q: 3. Is (3,8) a point on y = 3x - 1?

A: if (3,8) is a point on the line y =3x-1 then it should satisfy the equation y =3x-18=33-18 =9-18 =8…

Q: 5. If f(x)= kx³ + x² – kx+2, find k such that the graph of f contains the point (2, 12).

A: Given

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: f (2) 2. Find if Ar) -(1-x²)(* -1) =

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Q: 2P 2+ y= since) see' (=?)

A: y=sin(z)sec-1(1+zz2)

Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

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Q: Find the quadratic function y=ax2+bx+c whose graph passes through the given points.   ​(1​,−1​),…

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Q: briefly describe the steps involved in the new raphson method

A: We know that Newton-Raphson formula xn+1=xn-fxnf'xn where xn is the initial root. xn+1 is the root…

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Q: Section 1.5 Limits 59 Exercises 71-74, use a graphing mit (if it exists). 2+6x 7 72. lim x+2x-2 x-l.…

A: Given,

Q: 5. Determine the Wronskian of the functions (x)=x2 and g(x)=3x2. For what values of x is the…

A: Please refer to the image below