Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for...

Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for Simpson's Rule with n = 4 that approximates the integral of ln x on [1, 3].

Without doing numerical calculations, tell whether in approximating the integral of ln on [1, 3] by the Trapezoidal Rule with n = 8, the value T the Trapezoidal Rule gives is larger than, or is smaller than, the integral. Justify your answer.

Expert Solution

milcah answered 2 years ago

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

Let f(x)=x • 3^x a) Find formula for f^(n) •(x) for natural n (the n order...

Let f(x)=x • 3^x a) Find formula for f^(n) •(x) for natural n (the n order derivative). b) Write the Taylor series generated by f(x) in 0.

f(x) = x ln x (a) Write the Taylor polynomial T3(x) for f(x) at center a...

f(x) = x ln x (a) Write the Taylor polynomial T3(x) for f(x) at center a = 1. (b) Use Taylor’s inequality to give an upper bound for |R3| = |f(x) − T3(x)| for |x − 1| ≤ 0.1. You don’t need to simplify the number.

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the...

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the critical numbers of f . Find the intervals where f is increasing and decreasing. Determine if the critical numbers of f correspond with local maximums or local minimums. Find the intervals where f is concave up and concave down. Find any inflection points of f

Let F(x, y, z) = (6x5 ln(5y2 + 3) + 10z4) i + ((( 10yx6)/(5y2 +...

Let F(x, y, z) = (6x5 ln(5y2 + 3) + 10z4) i + ((( 10yx6)/(5y2 + 3))+ 8z) j + (40xz3 + 8y − 6π sin πz) k and let r(t) = (t3 + 1) i + (t2 + 2) j + t3 k , 0 ≤ t ≤ 1. Evaluate ∫ C F · dr (please explain steps, thank you :)

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

What is the minimum value of the function f(x)= (ln x) ^ln x for x >...

What is the minimum value of the function f(x)= (ln x) ^ln x for x > 1? A.) 1/e B.) 0 C.) e^-e^-1 D.) 1 E.) (ln 2) ^ln 2

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is...

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is of a fraction format) : a. has a stationary point at (1, 0) b. has a stationary point at (0, 0) c. has a stationary point at (0, 1) d. has no stationary points 2. Which of the following functions don’t have unit elasticity at P = 6? a. Demand: Qd = 24 - 2 P b. Demand: Qd = 10/P c. Demand: log...

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x). For each of the following statements, prove or disprove the statement. (a) For all relations R on X, if R is reflexive then S is reflexive....

Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...

Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 29 that lies above the plane z = 4 and is oriented upward.

Question