The function f ( x ) = cos( πx ) for x ∈ [0 , 1] is approximated by the following piecewise polynomial p of degree ≤ 3. The interval [0 , 1] is divided into k subintervals [ a j − 1 ,a j ] with a j = j/k for j = 0 , 1 ,...,k , and in each subinterval p is the polynomial interpolating f at 4 equally spaced points: a j − 1 , a j − 1 + 1 / (3 k ), a j − 1 + 2 / (3 k ), and a j . How should k be chosen so that the error max 0 ≤ x ≤ 1 | f ( x ) − p ( x ) |≤ 10 − 8 ? That is, derive an error upper bound, find the magnitude of | f (4) ( x ) | , and next get the desired value of k .

6.5

step-by-step explanation:

you said it was in the question

~courtney

$9.89

step-by-step explanation:

9.90 = p x .06 x .25 (3/12 changed to a decimal)

9.90 = p x 0.015

9.90 - 0.015 = p

9.89 = p

1.3 million hoops i believe

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places