Lagrange's Theorem If a function f(x) is continuous in the closed interval [a, b] and is differentiable in the open interval (a,b), then there exists at least one c belongs (a, b) such that f(b) – f(a) f'(c) = b - a

Q: Explain the Pythagorean Theorem, its proofs and applications.

A: The triangle is a polygon with three sides and three vertices. The sum of interior angles of a…

Q: tanx)-sinx) lis sintx) 1/2. -5/4 O 7/2 o 5/4 O

A:

Q: Define Lagrange Identity?

A:

Q: (3) a) Prove that the following functions are harmonic and find for each function its harmonic…

A: Here we have to prove that the given function is harmonic function and also to find it's harmonic…

Q: d) Using Demoivre's theorem, show that, if z = e“, then i(:-" - ") sin no = ne N+ 2

A:

Q: Prove that tan 0 + 1 tan 0 1 A sin 0 where A is a single trigonometric ratio in terms of 0 to be…

A: To prove the given identity.

Q: Given the following sinusoidal function, which best describes the transformations that have…

A:

Q: 4) Verify the identity using the definitions of hyperbolic functions. e2x + 1 e2x – 1 coth x

A:

Q: I, (x, y) is any point on the __________ side of theta when in standard posi- tion, and r is the…

A: Complete the blanks in the statement.

Q: Need answer using Laplace

A:

Q: Dzi "Use Bessel's functions to solve the following CDE in terms of trigonometric functions. x ² y ₁…

A:

Q: Shift Operator, Forward & Backward Difference Operator

A: We have to solve the given expression  ∆2E∇3e16xsin37x

Q: Derive the formula cos(a)=cos(b)cos(c)+sin(b)sin(c)cos(A) for an arbitrary spherical triangle with…

A:

Q: The trigonometric function is defined by ƒ(x) = 2sin4(x-7)+4 a) tate the transformations and key…

A:

Q: If two straight lines are mapped by a bilinear transformation onto circles tangent to each other,…

A: To Determine :-  If two straight lines are mapped by a bilinear transformation onto circles tangent…

Q: 3) S] Another Ferris wheel at a local fair has a radius of 13m, and is 1 m above the ground at its…

A: Ferris Wheel has a Radius of 13 m. 1 m above the ground at its lowest Point. The Ferris Wheel makes…

Q: use demoirvre's Theorem of powers z= Square root 2 (cos 5 pi/24 +i sin 5 pi/24)

A: Given : z=2cos5π24+isin5π24 de moivre's theorem: If z=rcosθ+isinθ then zn=rncosnθ+isinnθ.

Q: Use Euler’s Formula to find ii

A: we know that  i=eiπ2 so, ii=eiπ2i=ei2π2                                                  ∵…

Q: Use De Moivre’s theorem to write (cos π/5 + i sin π/5)^5 in the form of a +bi

A:

Q: Formulate the Fundamental Theorem of Algebra.

A:

Q: cos x D. Explain why we cannot apply L'Hôspital's rule to evaluate lim x-0

A: Given query is to find why L'hospital can not be used.

Q: w=tan inverse[ ((1-z)/(1+z)) ] is a complex function, what is the mapping conformal  of unit circle…

A: We will find the first seethe image of (1-z)/(1+z) when IzI=1

Q: cos () da. COS

A:

Q: 18 sin=+icos- 3.

A: Given complex number is sinπ6 + icosπ618

Q: Find the exact value of Cot (). 5л 12 Show all your work!

A: Given,            cot5π12

Q: (b) State Heine-Borel Theorem.

A: (Heine-Borel Theorem). A subset A of R is compact if and only if A is bounded and closed (with…

Q: in corred не все EX) = (хес C

A:

Q: State the inputs and outputs for arcsin (also stated as sin¹). Explain why the angles for this…

A:

Q: f-A Sin(b2) cos (but) Does aboue ginen en funchion Saitsy the follewingS Saidsfy the following…

A:

Q: the question says without using Cauchy Riemann equations.

A:

Q: Giveni- The fourier Seviej a fIt)= Sin ht TT n=1,3,5,.. find: a +6

A: We know that the Fourier series of a function f(x) defined on the interval 0, 2L is…

Q: (vz dis ) 6 2 cis 18 57

A:

Q: can anyone claim and explain the Perro- Frobenius theorem, and show an example of it, like step by…

A: