b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

A:

Q: d -1 ) Prove that cos 1(x) : dx V1-1

A:

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = cos x −…

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the equation in the given…

A:

Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

A:

Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

A:

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

A:

Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

A:

Q: Determine whether the pair of functions are linearly independent. f(x)=pi,…

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Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

A:

Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: In Exercises 7-12, compute the derivative.a(0) = (cos 30)i + (sin2 0)j + (tan 0)k

A: Given that, aθ=cos3θi+sin2θj+tanθk      ...(1)

Q: Obtain graphically an approximately value of the root of x = sin x + Tt /2

A:

Q: Use the Fundamental Theorem of Calculus,Part 1, to find the function ƒ that satisfies the…

A: We have to use the fundamental theorem of Calculus Part-1 to find the function f that satisfies the…

Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

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Q: Find the absolute maximum of the function f(x)=sin(2x)+cos(2x) on the interval [0, pi/6].

A:

Q: Graph the following vector fields

A: (a)known fact:

Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

A:

Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: Show that (Aetkx + Be-ikx)and (C cos kx + D sin kx) are equivalent ways of writing the same function…

A: eix  = cos(x) + i sin(x) e-ix = cos(x) - i sin(x)

Q: Show that cos A x e 2 *,x2 0. %3D

A:

Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

A:

Q: Is the function A cos (ka - wt = psi) a function of the operators ^ E and ^ T?

A: yes this is true

Q: Use the intermediate value theorem to show that there is at least one real root of the equation cos…

A: Given: cosx=x3

Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

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Q: Find the function f(x) such that f''(x) = 6x + 3 cos(x), f(0) = 5, and f(1) = 2 − 3 cos(1).

A:

Q: Verify Initial and Final value theorem for the function. f(t) = 2 + 3 cos t.

A: Given function is ft=2+3cost. We have to verify the initial and final value theorem. Initial value…

Q: Express f(x) = 2cos3x + 2sin3x to the form f(x)= a cos(bx+c) and determine the amplitude, period,…

A: Here we have to express f(x)=2cos3x+2sin3x to the form f(x)=a cos(bx+c) and also determine the…

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: Use the Intermediate Value Theorem to show that in the interval [0,1] the equation below has a…

A: Given that: sinx=2x-1

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: If f(x) = 6 sinx + 6 cos a, then %3D f'(x) = %3D f'(4) = %3D

A: Simply take the derivative using standard derivative forms.

Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

A:

Q: Use the Second Fundamental Theorem of Calculus to evaluate cos (E) dx.

A:

Q: Cos X 2)

A:

Q: 15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e…

A: 15.  a) Given, e2x, 3x Now the Wronskian is, Wf, g=fxgxf'xg'x=e2x3x2e2x3=3e2x-6xe2x≠0 Since the…

Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

A:

Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: Verify whether the function u=e^(x^2-y^2 ) cos⁡2xy is harmonic or not.

A: A function u=fx,y is said to be harmonic if ∂2u∂x2+∂2u∂y2=0 Now, we have u=ex2-y2cos2xy We will use…

Q: Prove that d/dx [cos x] = −sin x.

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Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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Q: Determine the value of a for which the function F(x,y) equation Fr - aFyy= 0. 8. cos(2x) cos(6y)…

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Q: Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(C

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.