1. drxln(x) (r+2)(x+4) ; 2. drxrª (x+3)(r+5) 0 < a < 1

Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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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: If if x 1

A: Given To Evaluate (g o f)(-1)

Q: (b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x 2 Find the value of ß so that f(x) is continuous…

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Q: How can I show that f(x) is O(x2), where f(x) = 6x2 + x + 1

A: Given: f(x) = 6x2 + x + 1

Q: In Problems 21–32, tell the maximum number of real zeros that each polynomial function may have.…

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

Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: Prove that for x≠0 the inequality ex&gt;1+x holds.

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Q: Find the particular solution determined by the initial condition. 2/3 f'(x) = 3x - 6x; f(1) = - 7…

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Q: 7. There is aremovable discontinuity at x = 1 andf(1) = 4

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: . If f(x) = 3x find the image and preimage of 6.

A: Given: fx=3x To determine: Image &amp; Preimage od 6.

Q: 2. Determine all x ER that satisfy each of the following inequalities. (c) 지 + \x- 1| <3 (d) |x– 1|<…

A: We will find out the required solution.

Q: 14)- Consider the following formula f"(x.) = 4-4o+3f-1 _ 2hfm(c) 6h2 3 Find the optimal h.

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Q: do you agree with the contention that the funtion f(x) = x + 2 and g(x) = x² − 4/ x -2 are the same.

A: Given f(x) = x + 2g(x) = x2-4x-2

Q: In Problems 11–20, use the Remainder Theorem to find the remainder when f1x2 is divided by x - c.…

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

Q: How would you remove the dis . z46 f(r) =

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Q: 3 If f (2) = -5 and f'(2) = – find [f-1]'(-5). %3D 4

A: topic - derivative of inverse function

Q: Let f(2) = x² +1 and g(z) = z² - 1 Then (fo f)(z) -X (fo g)(x) (go )(x) : x*4-x^2+1 x*4+x^2-1 Note:…

A: Consider the following functions: fx=x2+1gx=x2-1 ffx=x2+12+1=x4+2x2+1+1=x4+2x2+2…

Q: 2x : 1 3 is not one to one True False

A: Given: The function f(x)=2x : 1≤x≤3x   :  x&gt;3

Q: if x 0 -

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Q: 2 is the graph of f(x) = -2/3 x – 3. -6 -5 -4 -3 -2 -10 1 2 3456 -2 -3 -4 -5 O False True

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Q: 1- x**! 1- x n+1 6 (x # 1) r=0

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Q: 3. Given that g(x) =7x-6 and f(x) =x+1, then the domain of |(x) is O{r\x&R} O{r|x+-1, xɛR} xɛR 6 -1,…

A: First I have written the definition of qutient of two functions and tell about their domain. Option…

Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: Suppose that 2 ≤ f '(x) ≤ 3 for all values of x. What are the minimum and maximum possible values of…

A: Given , Suppose that 2 &lt;= f’ (x) &lt;= 3 for all values of x. The minimum and maximum possible…

Q: 3 2 y X-3x-x t3 From X = -1 to X= 8

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Q: Show that f (x) = 3x² - x - 1 is O(x²) with suitable C and k.

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: Prove that for x&gt;0 the inequality lnx≤x−1 is true.

A: Given data:     The given inequality is: . The given expression can be written as, Here, f(x) is…

Q: 4 if x 2

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Q: 4. There exists c between -2 and 1 such that f(c) = 3. (a) must be true (b) must be false (c) could…

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Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: 5 2 7 . If f(x) = 3 + 4x · 2* + r", what are f"(0) and f"(0)? 3!

A: Given f(x)=3+4x-52!x2+73!x3

Q: 1. -x+2 4. if x<-1 h(x) = (x-1) - 3 if -13XS2 -2 if x 2 Th(1), h(2), and h(5)

A: Given that hx=14x+2 if x&lt;-1x-12-3 if -1≤x≤2-2         if x&gt;2 find h1, h2 and h5

Q: evaluate x2 -(xy-y) for x satisfying x/9 -7 = x/2 and satisfying -3y -5=4y+23

A: See the details solution in below

Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

A:

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: 4. If the domain of f(x) is -35x59 and the range of f(x) is 25ys15, then which of the following…

A: Here we can use the concept of transformation of function as for given function f(x) the…

Q: If f(4) = 3 and f'(x) 2 3 for 4 s xs 9, how small can f(9) possibly be? (9) 2

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Q: In Problems 21–32, use Descartes’ Rule of Signs to determine how many positive and how many negative…

A: Use Descartes’ Rule of Signs to determine how many positive and how many negative zeros each…

Q: r(x)=x-2/x^2+2x+1 As x right arrow - infinity, r(x) right arrow As x right arrow infinity, r(x)…

A: Taking highest factor common from denominator and numerator evaluate the following limit

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

A:

Q: Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of…

A:

Q: ) Show that |2x - 2|-|x+1| +2≥0 for every x € R.

A:

Q: 3 By applying the Intermediate Value Theorem choose the interval over which x4 = 7x3 - 5 will have a…

A: The given problem is to find the interval for the given function that which the intermediate value…

Q: = 1 – _X k – 1 k + 1

A: We can eliminate the arbitrary constants as below.

Q: Suppose that 2 sf (x) < 4 for all values of x. What are the minimum and maximum possible values of…

A:

Q: 2 If f(x) = 2(1 – x)-1. | 1-x Find a formula for f(n) (x).

A: The given function is:  fx=21-xfx=21-x-1 To find the formula of nth derivative fnx, evaluate the…

Q: In Problems 13–16, give on its domain. 13. f(x) = 2x² - 3

A: we have to write