Question

Use multiple-application Trapezoidal rule with ? = 4 to estimate
the value of tan^{−1}(2).

Answer #1

Use the trapezoidal rule with 4 rectangles to estimate the
integral of ex^2 dx from 1 to 3

Use the trapezoidal rule with n=4 steps to estimate the
integral.
Integral from -1 to 1(x^2+6)dx
(-1 is on the bottom)

Use the Trapezoidal Rule to approximate 4 on top ∫ on bottom 2
(9x^2+1) dx using n=4. Round your answer to the nearest tenth.
Evaluate the exact value of ∫42(9x2+1) dx and compare the results.
Trapezoidal Approximation ≈ Exact Value=

(a) Use the Trapezoidal rule with 4 equal partitions to
approximate
?
integral (from -1 to 1) (x^2 +1)dx
via the formula Tn =(∆x/2)(y0+2y1+...+2yn−1+yn )with n=4, and
∆x=(b−a)/n
(b) Compare the actual error, found by direct integration minus
the approximation, with the known error bound for the Trapezoidal
rule
|ETn| ≤ (f′′(c)/12n^2) (b−a)^3, 12n2
where c is a point at which the absolute value of the second
derivative is maximized.

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 4 0 ln(5 + ex) dx, n =
8
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule

Use the trapezoidal rule with n = 4 to approximate the integral
with a upper bound of (1/3) and a Lower bound of 0 1/3 ∫ √ (1- 9x^2
)dx
******* by the way square root covers 1- 9x^2 in the integral
fully for the entire equation
b. ) Use Simpson’s rule with n = 4 to approximate the same
integral.

Use the Trapezoidal Rule to approximate 8 on top ∫ on the bottom
5 ln(x^2+4) dx using n=3. Round your answer to the nearest
hundredth.

Find M of the following integration and find the relation error
use the trapezoidal rule to approximate the definite integral.
Use n=4

Estimate the minimum number of subintervals to approximate the
value of Integral from negative 2 to 2 left parenthesis 4 x squared
plus 6 right parenthesis dx with an error of magnitude less than 4
times 10 Superscript negative 4 using a. the error estimate formula
for the Trapezoidal Rule. b. the error estimate formula for
Simpson's Rule.

A) Prove the trigonometric identity
(tan x + 2)^2 = sec^2 x + 4 tan x + 3
B) Use a sum-to-product identities to show that
cos(x + y) cos x cos y = 1 − tan x tan y.
C) Write the product as a sum
Sin12xSin4x

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