Suppose that the functions s and t are defined for all real numbers x as followS. s(x) =x+2 t(x) = 3x %3D Write the expressions for (s - t)(x) and (s +t)(x) and evaluate (s-t)(-3). %3D (++ :)(-) = ] (6-)(-)) = ] %3D

Q: Use the graph of f(x) = x3 + 3x2 - 4 in the figure given to factor x3 + 3x2 - 4.

A: Given function: And the graph:

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: f(x) = x4 + x - 6 ƒ is continuous over the closed interval [a, b] if and only if it's continuous on…

Q: If the bound of error greater than zero, the polynomial is------than the .function not equal O its…

A:

Q: Find f"(x). 13. f(x) = x³ – . 3 14. (x) = x* + 15. f(x) = x'/5 16. f(x) = x'/3 17. f(x) = 2x-2 18.…

A: As there are multiple questions 13 is solved here.

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

A:

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(-2) = 3.

A:

Q: 7. If f(x) = mx²-x+2 and g(x) = 3x² +nx-4, and the points (-2, -14) and (1, -11) are on the combined…

A:

Q: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

A:

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| <

A:

Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| < |3

A: Given that |x2-1|&lt;13 That is -13&lt;(x2-1)&lt;13

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7…

A:

Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: Find critical number of f(x)=x^3-6x^2

A: Given: f(x)=x3-6x2

Q: 1. prove that if x is real number then ,[2x] =[x] +[x +1/2] when [x] denote the greatest integer…

A:

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

A:

Q: Show that when x increases from 1 to 1.25 and when it increases from 2.75 to 3, the value k of grows…

A:

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

A:

Q: 1 The volume, V, of a rectangular box with a square base and height h inches can be mode by the…

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Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Since x^4+x-8 is a polynomial it is continuous.Answer: f(x)=x^4+x-8 is continuous on the closed…

Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: Suppose that 0 &lt;ƒ′(x) &lt; 1/2 for all x-values. Show that ƒ(-1) &lt; ƒ(1) &lt; 2 + ƒ(-1)

A: From the given inequality the behaviour of the function can be determined as.

Q: Determine f-¹(x) if 1 (X) = Or¹(x)=x2 X+2 X-3 X-2 or¹(x) X+3 Or¹(x)= X-1 3x + 2 3x + 2 X-1 OM(x)=)…

A:

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: 1 If f(x, y, z)= of then x- y- 3z ду а. 1 (х— у-3-)* b. -1 | (х-у-3-)? С. (х — у-3-)? d. 1 (х-у-3-)2

A:

Q: (i) Show that f(x) = 6x³ – 2x2 + 4x – 3 has exactly one real root. (j) Show that f (r) = x + 2x5 +…

A: Given: i. fx=6x3-2x2+4x-3ii. fx=x7+2x5+3x3+14x+1 To Show: Given equation has exactly one real roots.…

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: (1) Find and classify the extreme values of f(x) =6x* -4x over the interval [-2,2].

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 1. The interval for function |2-3x|>5 is 0(-1,7/3) (-00,-1) u(7/3,00 ] (-00,-1) u(7/3,00 ) O[-1,7/3]

A:

Q: Find all zeros. f(x) = x^4−x^2−30 f(x) = x^4+ 2x^2−15 f(x) = 3x^3−7x^2−7x+ 3

A: Since you have sent more than 3 sub parts therefore according to our policies we are bound to answer…

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: Find critical number of f(x) = 4x^2 + 8x -1

A: We have to find critical number of  f(x) = 4x2 + 8x - 1 To find critical number, differentiate f(x)…

Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…

A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(1) = 0

A: We have, f'x=2x Integrating both of the side with respect to x, we get the result as…

Q: - Find all critical numbers of f(x) = 3x* + 20x – 36x²

A:

Q: Find any restrictions on x. ITS 1/2x - 5= 10

A: The given function is 12x-5=10 Solve 12x-5=10 as follows: 12x-5+5=10+512x=15x=30

Q: Let /(x) – x + 2x+ 3x + 4 € Z). Then x = -1 is a root for /(x) of multiplicity None

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Q: x^2 + 1/x^2 > 2

A: Here we use a property of real number which is square of any real number is non negative.