7. Let f(x) = 2x +3x2 - x- 5. Without forming the divided difference table, determine f xo, x1, X2, X3 and fxo, x1, x2, x3, x4. Justify your answer. (No credit is given if – X the divided difference table is used.)

Q: 2) Show that 2m +1 m P(x) m +1 -xP (x) m+1 (x)F

A:

Q: Given f (x) = ? - +, then f(x) is: 9. %3D Of(x) = - 15 | x4 Of(x) = - - – 4 15 x² 2. x4 Of (x) = -9.…

A:

Q: If f(x) = 1 4x - 1 384 (4x-1) 24 (4x - 1)¹ 24 (4x - 1)4 384 (4x - 1)¹ -, then what is f"" (x)?

A:

Q: 5 If f(x) = x + 2, evaluate f (3k +3). k=1

A: given :f(x)=x+2∑k=15 f(k+3)

Q: 12- If f(x)=v3x , g(x)=x/5, and h(x)=6x a. f(h(g(x))) b. f(g(h(x))) c. g(f(h(x))) ·

A:

Q: Let h(x)=f(x)−g(x). If f(x)=9x^2 and g(x)=8x, what is h′(−5)?

A:

Q: Let f(x)=3^4x and g(x)=3^4x^2. Which value for xsatisfies f(x)=3⋅g(x

A:

Q: 4. Compare and contrast f(x) and g(x). g(x) ={-x - 3, when r< -2 (x+ 1, when x2-2 f(x) = |x + 2| + 1

A:

Q: (b) Let the function f: R → R defined by 3x for x > 3 2x2 + 3 for - 2 < x< 3 3 x? – 7 for x<-2 f(x)…

A:

Q: Let h(x) = f (X)g(x). If f (x) = In(3x² - - 4) and g(x) = 3x – 1, what is h' (x)? Select the correct…

A: Here, the given function is: h(x)=f(x)g(x)

Q: 2x If f(x) = then x3 – 729 -1458 – - 4x3 f'(x) = and (x3 (23 – 729)? 12x + 17496x2 ,5 f" (x) Where…

A:

Q: 4 Suppose that f(x, y) = x4 + y xy

A:

Q: P(4<X<5)

A: Given that X is a continuous random variable. The probability density function is given as, fx=x8…

Q: - Which of the following is not a possible f(x) = 4x - 2x + 10? 5 3 3, 5, 22

A: Given f(x)=4x5-2x3+10 Let x=3,  f(3)=435-233+10       =4(243)-2(27)+10=972-54+10=928≠0 3 is not a…

Q: is If f(x) = x² + 4x + 4 , then the domain of y = A(x) {x\x +- 2,2, x ER} {x\x +- 2, x E R} А. В. С.…

A: 1. (2) Range of the function y=f(x). From the above figure of the graph shown, the range of y=f(x)…

Q: 14 7) If f(x) = T4x-5) find f"(x) %3D

A: Given function is- f(x)=14(4x-5)27We need to find f''(x)First we will find f'(x) f'(x)=ddx14(4x-5)27…

Q: Determine the extreme values of the ff. functions. f(x) = x^2 -8x +12 on [-5,3] f(x) = -2x^2 + 12x…

A: Given: fx=x2-8x+12 ; x∈-5,3   As we know that; For maximum and minimum values, differentiate the…

Q: (4) Find the domain of f(x) = Vx3 – 2x² – 24x. (A) [-4, 0] (B) (6, ∞) (C) [-4, 0] U [6, ∞) (D) [-4,…

A:

Q: If f (x) = x²cos-(x² – 4), what is f'(x)? 2x3 o f'(x) = 2xcos-'(x² – 4) – V 1-(x²-4)² 2x3 o f'(x) =…

A:

Q: 2. Given : f(x) = {x² - 3, x+3 6, %3D X = 3

A:

Q: 3 5 If f(x) = 2 – 6(x - 1) +(x – 1)2 – ¬(x – 1)3 + 2! 3! 1 -(x – 1)“, what are f"(1) and f'(1)? 4!

A: Given that, fx=2-6x-1+32!x-12-53!x-13+14!x-14 Then we get,…

Q: If f(x, y) = (3x³ + 2y² – 12)', then fy is given by : 6. O 42 y (3x³ + 2y² + 12)° O 28 y (3æ³ + 2y²…

A: fy: Partial derivative of fx,y w.r.t. y Keeping 'x' as constant.

Q: 4. If f(x) = x* + 3, g(x) = x – 1, h(x) = Va, then fogoh(x)= %3D

A: fx=x4+3, g(x)=x-1, h(x)=x

Q: 2 9. If f(x) =-(x- 5), determine the following %3D 3 f(17)- f(8) а) 17-8 (12)- f (4) b) 12 - 4

A: The given function    f(x)=23x-5

Q: 1 For what, if any, values of a will f"(x) = 0 if f(x) = + x – 2.r2 + 17? %3D -3 V21 3土V21 3 3 O…

A:

Q: 3. Given f (x) = x2 - x + 16. If f (w) = 12, what is the value of w?

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

Q: 14. If Ax) = X+3 and g(x) =x² + 5, what is f(g(4))? 2

A: We know that  (fog)(x) = f(g(x))

Q: 17. If f(x - 1)+ 2/(1 — х) %3 3х, what is f(x)? А) -Зх + 1 В) х—3 С) -х +3 D) -3x – 1 |

A:

Q: 3. Use the definition of "f (x) is 0(g(x))" to show that x4 + 9x³ + 4x +7 is O(x4).

A:

Q: Show that x - c is not a factor of f (x)for anyreal number c.

A: We have given fx=-x4-3x2-2 We can see here fx&lt;0 for all x belong to set of real numbers. If x-c…

Q: 522 — 20, х 2 ||

A:

Q: _6. If f(x) = 18x² and t(x) = 8x, find_£(x). t %3D а. 9х 4 b. 4x 9 c. 4_ 9x d. 9 4x _7. When f(x) =…

A: Topic :- Functions

Q: 7.If f (x) = x³sinh(2x) then f'(x) = -1

A: Explanation of the answer is as follows

Q: Show that (x) = In/x² -1- In /3, f"(x) = 1 and (2) = 0. .2 x* - 1 | Justify your answer.

A:

Q: 2 If f (x) =x² and g(x) =x – 5 then f(g(x))= x² + 25 x² – 25 O x²-5 O x² – 10x + 25

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

Q: 4. If the function f is defined by f(x) = 5x + 3, then 2f(x) + 1 = %3D %3D 7x+4 В 7x+7 10x+4 D 10x+6…

A: If the function f is defined by f(x)=5x+3, then 2f(x)+1=

Q: Suppose that f(x) is O(g(x)). Does it follow that 2f(x) is O(2g(x))?

A:

Q: If f(x) = 5x - 2, g (x) = – 2r + 3 and h (x)= x, then (fogoh)(-2)=.... %3D

A: The functions are f(x)=5x-2g(x)=-2x+3h(x)=x3 If f(x) and g(x) are two functions then the composition…

Q: If f(x) = 5x2 - 4x and g(x) = 4x, find (g ∘ f)(x). a 5x2 - 8 b 20x3 - 16x2 c 20x2 - 16x d 80x2 - 4x…

A:

Q: 4 given that g(2) =1 and g'(2)= - 5, what is F'(2)? If F(x)= g(x)*

A: Just use the quotient rule of derivative and get the required solution. F'(2)=20

Q: 30. Show that if F = xi + yj + zk, then ▼ X F = 0.

A:

Q: 21 If fx)3then f(x) O 2x-2-1 3x 2x-3r2-3 3x O 2x-3x2-3 6x 2x 3x+2 O 2x-x2-1

A: Find the derivative of the given function.

Q: Suppose / (x) =2* +. Evaluate: /f(x) dr A 3.23* +1, In (2) +C 23x +1. In (2) +C B 3 3.23x +1 -+C In…

A: Topic = Integration Correct option = D

Q: Which is true for the A. f(x)= In(4-2x) -1 f (x) = 4-2x B. f(x)= In 4-2x C. f(x)=/in(4-2x) D. f(x)=…

A: dlnax+bdx = a.1ax+b dax+bndx=anax+bn-1

Q: Do you agree with the contention that the gunctions f(x) = x + 2 and g(x) = x2 - 4 ÷ x - 2 are the…

A: Function f(x)=x+2As we know that domain of a function is the set of input or argument values for…

Q: How can I argue that f(x) is not O(x), where f(x) = 4x2 + 1?

A: We have to prove that fx=4x2+1 is not Ox. By definition, we say that fx is not Ogx if and only if…

Q: 4 If f(x) = x* + 6, g(x) = x – 7, h(x) = Va, then - fogo h(x)=

A: This is composite function so solve inner first than outer.

Q: 12 Given that f(x) = 5x +4 and g(x) = 7-z, calculate (a) f(g(0))= (b) g(f(0))=

A: Given that, f(x)=5x+4g(x)=7-x2