Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every where.

Q: Examine the differentiability of the function f(x)=|cosx| at z 2 %3D

A: Given: f(x)=|cosx|

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

Q: Determine the local extrema of the function f(x)=sinx−cosx on [0,2π].

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Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

Q: Show that the function e (cos y +i sin y) is holomorphic (anal ytic) and findits derivative.

A: u(x,y)=e^x*cos(y) and v(x,y)=e^x*sin(y) We prove Cauchy Riemann satisfy everywhere

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: Perform error analysis of approximation derived (a) 1 x² 1 - at xo = 0 X (b) sin (₁) ₁ X- at x = = 0…

A: Given that: a 1x2-1 at x0=0b sin xx-1 at x=0c exp x2-1 at x=1 and x=-1 The objective is to analyse…

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Q: Show that the function ex(cos y +i sin y ) is holomorphic and find its derivative

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Assume that y is a differentiable function of r such that y² = x² + 4x sec y. Find y' by implicit…

A: implicit differentiation

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. cOS X y =…

A: To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.y=∫sin…

Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

A:

Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Let f : R→ R be a differentiable function. Then for all x € R, the derivative of f ( sin (4x)) with…

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Q: Prove the differentiation formula d/dx [cosh x] = sinh x

A: We use the formula of coshx to find the derivative

Q: (A) Prove that: cosh x + sinh x = e*

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Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: x+y are functions of t.Ue %3D Ronphicit differentiation to express in terms af dx X and y dy

A: Explanation of the solution is given below....

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: Find an analytic function whose real part is e-x(x sin y-y cos y )

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Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

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Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

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Q: 4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

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Q: Prove that: sin z = sin x cosh y +j cos x sinh y

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the absolute maximum and minimum values for f (x, y) = 4 sin(x) + 9 cos(y) on the rectangle R…

A: Given that: fx,y=4sinx+9cosy Limit: 0≤x≤2π, 0≤y≤2π We know that if a,b is a critical point and…

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: Find the absolute maximum of the function. fAx) = sin(6x) + cos(6x) on the interval 0. 18 %3D

A: Given: f(x)=sin(6x)+cos(6x) Differentiae the function.…

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

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Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h (x) =…

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Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: Find the most general antiderivative. Verify with differentiation f(x)=cosx + 2sec^2x

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Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

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