How to use Maple to solve calculus equation

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1. High score with maple to do a calculus problem! Consider the following function on the interval [0, π/2]. f (x) = √ 2x cos8(2x) (a) approximate the area under F &; (x) on the given interval using midpoints with n = 10 (b) compute the definite integral of F ｛ 8201; (x) on the interval [0, ｛ 8201; π / 2] (c) find the absolute value of the error involved in estimating the area under F &; (x) on the given interval using a Riemann sum with midpoints and N = 10 (d) Using trial and error,determine the smallest number n of subintervals such that the absolute error of the midpoint Riemann sum with respect to the exact value of the area is less than 0.0005. 2X times (COS (2x)) ^ 8 under the root of the equation
2. What is the running result of maple ('a: = ', 245674)
3. If Tan θ = 2, then the value of 1 / (Sin & # 178; θ - cos & # 178; θ) is
4. Sin α + cos α = 1 / √ 2 find the value of Tan & # 178; α + 1 / Tan & # 178; α
5. If Tan a = 2, then the value of Sin & # 178; a / (1 + cos & # 178; a) is?
6. Tan α = 2, find the value of [(sin α + cos α) / (sin α + cos α)] + cos & # 178; α
7. Use Maple to solve the equation x^5+x^4−12x^3−21x^2+x+5=0 y^5+y^4−16y^3+5y^2+21y−9=0 y^5+y^4−24y^3−17y^2+41y−13=0 y^5+y^4−28y^3+37y^2+25y+1=0 10x^6-75x^3-190x+21=0 All the previous quintic equations have radical solutions The last one, I don't know if there is. If there is, we need radical solution No, I hope it can be solved with a special function, like this z^5+z^4-e^6=0 z=exp(6/5)*hypergeom([-1/5,1/20,3/10,11/20],[1/5,2/5,3/5],256/3125*exp(-6)) +2/25*exp(-6/5)* hypergeom([1/5,9/20,7/10,19/20],[3/5,4/5,7/5],2/3125*exp(-6)) -4/125*exp(-12/5)* hypergeom([2/5,13/20,9/10,23/20],[4/5,6/5,8/5],256/3125*exp(-6)) +7/625*exp(-18/5)* hypergeom([3/5,17/20,11/10,27/20],[6/5,7/5,9/5],256/3125*exp(-6)) -1/5
8. On the proof of matrix complex field, we will add 1-2 times points Let a be a matrix of order n over a complex field 1) A is similar to a matrix in the form of: λ1 c12 c13 ... c1n 0 λ2 c23 ... c2n 0 0 λ3 ... c3n ... ... ... ... ... 0 0 0 ... λn 2) A has n eigenvalues (multiple roots count multiple numbers) in complex field, and if λ 1, λ 2,..., λ n are all eigenvalues and f (x) is any polynomial in complex field, then f (λ 1), f (λ 2),..., f (λ n) are all eigenvalues of F (a)
9. Let a be a matrix of order n over the complex field C It is proved that there exists an invertible matrix P of order n on C such that P ^ - 1AP = R1 A12. A1N 0 a22 .a2n . 0 an2 .ann
10. Higher algebra A is a matrix of order n over a complex field, R1, R2,..., RN are all eigenvalues of a (multiple roots are calculated by multiplicity) proof (1) if f (x) f (R1) The higher algebra A is a matrix of order n over a complex field. R1, R2,..., RN are all the eigenvalues of A. This paper proves that (1) if f (x) is a polynomial of degree greater than 0 on C, then f (R1), f (R2),... F (RN) are all the eigenvalues of F (a). (2) if a is invertible, 1 / R1, 1 / R2,..., 1 / RN are all the eigenvalues of a ^ - 1
11. Various methods of finding limit and calculus,
12. Maple / Matlab symbolic operation There is a problem for a long time Is there any way to define an n-dimensional vector (or matrix) in MATLAB or maple, but n does not need to be assigned, and then symbolic operation? For example, I need to derive a function: l = 0.5 * w (T) · V · W, Where W is a variable, an n-dimensional vector, w (T) is its transpose vector; V is an n * n coefficient matrix; n > 1 is an integer In the symbolic operation of maple or MATLAB, can l be derived without n assignment? The derivation of L is very simple. It's a general formula. The problem is how to do symbolic operation on a general formula like this in the program?
13. How to calculate the binary value of 110.110... With maple 110.110... Is a decimal with infinite cycles
14. cos(a+β)=3/5,cos(a-β)=12/13,0
15. First, cos (a + b) = 4 / 5. Cos (a-b) = - 4 / 5. A + B ∈ [7pi / 4,2pi]. A-B ∈ [3pi / 4, PI]. Cos2a =? Second, prove tan（ The second problem proves that Tan (θ + π / 4) = [Tan θ + 1] / [1 - Tan θ]
16. Cos (a + b) = 12 / 13, cos (a-b) = - 12 / 13, and A-B belongs to (PI / 2, PI), a + B belongs to (3pi / 2,2pi) find cos2a-cos2b
17. Under the simplified radical [1-cos (a-pi)] 2 -3pi
18. It is known that cos (a + (1 / 4) PI) = 3 / 5 and PI / 2
19. Given that a and B are acute angles, and sin (a + b) = 4 / 5, cos (a-b) = 3 / 5, is the first sin2a of sin2a and cos2a equal to 24 / 25?
20. If cos (π / 4-A) cos (π / 4 + a) = (√ 2) / 6 (0 < a < π / 2), then sin2a =?