2. Prove that there exists a polynomial p(x) such that and 2π * P(a)sin(a)dx = 2π 1 | S*"* P(z)sin(n.z),de| < 1,000,000 dx Hint: cos(-y)-cos(x+y) = sin(x) sin(y). ( 2 for n = 2, 3, 4, ...

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

A:

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: Let f(æ) = sin(x) and g(æ) = x² . Find (go f)'(x) O 2sin(x)cos(x) O 2xcos(x?) -2æcos(x?) 2xcos(x)

A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i…

Q: (A) Evaluate Sin (3x) Sin (3x) dx

A:

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: Let f(x) = sin(2x) + cos(x) then f"(x) Select one: O a. 4sin(2z) + cos(z) O b. -sin(2x) – cos(x) Oc…

A:

Q: sir(*) F(x) = ["cos (?' )at # 26 If find F'(x). (A) cos(x) cos (sin'(x)) (B) cos (sin'(x) }in(x) cos…

A: Leibnitz Rule of differentiation:       ddx ∫α(x)β(x) f(x,t) dt =∫α(x)β(x) d(f(x,t))dx dt +d(β(x))dx…

Q: Pr. #1) Find the exact value of So f(x)dx using the graph of f below.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

Q: prove the following identities: cos² (y) - sin² (y) 1 - tan² (y) = cos² (y).

A: according to bartleby guide line we do only first part of multiple questions prove…

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

A:

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

A:

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: (1) (sinz) + (cosr)* sin x COS x (2) tan x in terms of sin x, cos x %3D d. d. ( sin x COS X %3D dx…

A:

Q: Use the simplex method to solve the linear programming problem. Z=4x₁-3x₂ + 2x3 2X₁ X₂ + 8x3 ≤ 42…

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Q: . What is F(/3) if C = 0?

A:

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: -tan (m + 1)(x) + C tan I + m um + ( x ) (x + ₁)² I m+3 1 с

A: Using substitution then integrating we get correct answer as (C)

Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

A:

Q: . Express the function F(x) = 1 + sin x 1+ sin² x in the form (fog)(x).

A: