1. Determine if the following statements are true or false. If it is false, explain why. (a) fesle) da = e"f(e) - fete)dz + 2x (b) (x2 + 1)(x2 - 2) can be written in the form x2 +1 x2 – 2 4x2 - 15x - 1 (c) x(x2 - 4x 5) A can be written in the form B x +1

Q: . What is the coefficient of a" in (2 – x)"?

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Q: 4. If x²-2√3x + 1 = 0 then, a.Show that, x² - 2√2x-1=0. 14 b. Find the value of x¹4 +1 X X c. What…

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Q: Let h(x)=(x2−3x+2)/(−x2−4x+4,) what is h′(−5)? Do not include "h′(−5)=" in your answer. For…

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Q: Let h(x) -222+z+4 %3D ,what is h' (-5)? 2+4z-1

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Q: Solve the initi al value pro blem:s' (x)=Seckta nx-2X1F(0 23

A: Given: Initial value problem f'(x)=secxtanx-2x f(0)=3 Formula used: ∫secx tanx dx=sec…

Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: Let A = %3D {x €N|2 < x < 7|} . What is n(A)?

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Q: . Find a general solution for y" + 4y = x² by method of undetermined coefficient

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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: Show that the equation x4 + 4x + c = 0 has at most two real roots

A:

Q: Solve this problem using the indeterminate coefficients method: y" +2y' + y = 2cos(2x)+3x+2+3e^x

A: Given: y"+2y'+y=2cos(2x)+3x+2+3ex

Q: I am using this non graded study guide to prepare for an upcoming precalculus exam. Could you walk…

A: Given equation is,y = x3 + 1To find all the zeros of the equation, replace y with o and solve for…

Q: The intermediate value theorem can be used to prove that the equation x^2+7x+6=0 has at least one…

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Q: 17) Explain why these two quotients are different. Compute each one. (x – 2)* x* - 16 and X-2 x- 2

A: (a-b)2= (a-b)(a-b) and a2-b2=(a-b)(a+b)…

Q: 1. Determine the number on y=-x+3 2x-3y -24 %3D

A: The red line represents y=-x+3 , and the blue line represents 2x-3y=-24

Q: Q 4. (a). Show that fog = 4x² – 1, if ƒ(x) = 4x – 5 and g(x) = x² +1.

A: a. Given: The functions fx=4x-5 and gx=x2+1, To find: f∘g=4x2-1, Formula used: (f∘g)(x)=f(gx).

Q: 1. If 6x=l/a+1/6, show that (x+3a) (x-3a)+(x+3b)(x-3b)=2, a not equal to b.

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

Q: a'+3ab? If 3a’b+b³ 3x°y+y' _ x³+3xy² X_ y Prove that a b

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Q: 27 comp 28. 8 comp 29. +9° +90 27 = x2-6x 28 = 3x2 - y 3-x2 - 13x + 9 Find mz8. What is the name of…

A: Complementary Angles:- Two angles are complementary if the sum of the measures of both the angles is…

Q: show that the equation 3x+2cosx+5=0 has exaclty one real root.

A: f(x)=3x+ 2 cos x +5

Q: 2 Show 2 3 / 2

A: We have to solve the matrix.

Q: drp 2) r r +z 3/2

A: Given,             ∫0Rrr2+z232dr

Q: Given f(x) = √ x-4,   (the square root of x-4) Use the conjugate to simplify completely f(x+h) -…

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Q: 3. Suppose f(x) =. ) dr=AV 5x-4 +C, for constants. %3D If 5x-4 A and C, what is the value of A?…

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Q: If Æ(x) = 2x + 1, find Æ(a + h). 2a + 2h + 1 a + h + 1 2a + 2h + 2 2a + h + 1

A: Here we will find E(a+h),

Q: 2- The homogenous diff. equation can be put in the following form: B- y' f(x)

A: Here we will find the correct option,

Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: If k(x)= 2e^2x then k''(2) is equal to

A: Given  k(x)=2e2x To find  k''(2)

Q: ди ди ди AND az EXAMPLE: FIND əx' əy 5. 1= r2 + v2 + 72

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Q: Z1 and 22 are supplementary. Z1 = 124° 22 = (2x + 4)* What is the value of x?

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Q: 1(d) Show that x − 4 is a factor of x − 5x + 2x + 20x − 24

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Q: What is the fully factored form (with real coefficients) for the polynomial f(x) = æ® – 1? (Hint: 16…

A: Consider the given polynomial

Q: 19. What is the largest value of the quadratic form 5(x,)? - 3(x2)² if x²x = 1. 20. What is the…

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Q: Prove that there is a solution of the equation 2° + x² + 4 = 0, x in R.

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Q: 24 Use the diagram to solve for x, FG and FH. 4x 7x +6 FG = FH = 6 8 9 DELL -> 23 $ & 3 4 7 8.

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Q: 11. If f(x) = 2x² + 7x + 3, show that ƒ(b + 2) = 2b² + 15b + 25. %3D

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Q: 1. What is the coefficient of x²y5 in (2x – 3y)7?

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Q: Prove that the equation x- 15x +k = 0 has at most one root in the interval [-2, 2]. Hint: You'll…

A: Dear friend,  if you have any other query about this problem, then please tell me about your query I…

Q: Show that x^2 + 1/x^2 is greater than or equal to 2.

A: A.M  is greater than or equal to G.M

Q: The number of units in Z29[x] is

A: Solution by using definition of unit elements

Q: 8. If x* - 48x +1=0then, a. Provethat x - 5/2x+1=0 1 b. Find the valueof x- c. Showthat x 23030/23

A: Since you have submitted multiple questions, according to Bartleby policy I'll solve the first…

Q: Show that the equation x3 –- 15x + c = 0 has at most one real root in the interval [-2, 2]. |

A:

Q: 2. If f(x) = (x + 13)² +(x - 5)° + (x +5) , find f(3)- If necessary, use the Math Editor x to write…

A: our objective is to find f(3)

Q: 15. Show that (x+ 5) is a factor of f(x) =x3 -x² -21x + 45 then factor f (x) completely.

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Q: What

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Q: (x² + 4y² + 9) dr

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Q: Shon in Question 1.a find your mista y= -2x + 1 y3 -2x +3 y 2. -

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.