1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

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&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Find all points (if any) of horizontal and vertical tangency to the curve on the given interval

A: Given Data The first equation is x=cos θ+ θ sin θ. The second equation is y=sin θ- θ cos θ.…

Q: Find the maximum possible error in the computed value of the hyperbolic sine function, sinhx = at…

A: Solution

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: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

A:

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

A:

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = sec2 θ - cos(2θ) - 1, (0,…

A:

Q: Qs:- Prove that fez) = cx-g') + ( are harmonic function of (xy) ,but not hormonic conjugates.

A:

Q: What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral…

A: The derivatives of the six basic hyperbolic functions are as follows.

Q: Is this a possible way to show that f(x) = arctan(2(x-1)) - lnIxI has exactly four real roots?

A: What is Rolle's Theorem: Rolle's theorem is the base of mean value theorem. More precisely, the mean…

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

A:

Q: 2. F(x) = [ cosr' dt

A: Use fundamental theorem of calculus

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

A:

Q: (2) What are the derivatives of the six basic hyperbolic functions? What are the corresponding…

A: Hyperbolic functions are the trigonometric functions defined on parabola instead of taken on the…

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²-) < 0, ƒ (x) has a root in [0]. If we…

A:

Q: Find all points on the graph of the function f(x) = 2 cos(x) + cos2(x) at which the tangent line is…

A: Horizontal tangent is parallel to x axis hence slope of tangent is zero at that point

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

A:

Q: Use linear approximations to estimate the following. 1. sin 9/4

A:

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

A:

Q: 5. Express lim 2 cos as a definite integral, then find t

A:

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A: NOTE:Use the form y= asin(bx−c)+d to find the variables used to find the amplitude, period, phase…

Q: Find all æ values on the graph of f(x) = 2x – 4 cos æ for 0 < a < 2n where the tangent line has…

A:

Q: Determine the real root of the equation r sin(x) + cos(x) = 0 in the interval (2, 3) by using…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: Sketch the graph of two functions g(x) = cos x and h(x) : plane. Choose [a, b] that satisfied |b –…

A: Given function is g(x)=cosx and h(x)=x/2

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: Find all points (if any) of horizontal and vertical tangency to the portlon of the curve shown x-…

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: 3. Find the root of the function x) - sin x +xe between -3 and -4. using Bisection and Newton's…

A: We have to find the root of the function fx=sinx+xex in the interval using the Bisection method. We…

Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

A:

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: Use the Intermediate Theorem show that there is a root of the given equation: sin a - x between…

A: Intermediate value Theorem states that if f is continuous on the interval (a ,b ) and L is a number…

Q: I* cos z lim 1³+2

A:

Q: 1. Determine the real root of the equation r sin(r) + cos(x) bisection method with 3 decimal places…

A:

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: Find all points on the graph of the function f(x) = 2 sin(x) + sin2(x) at which the tangent line is…

A: Tangent line

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

A:

Q: 5. Find the slope of the graph of cos(x + y) = 2x at the point ( 0, n/2 ). Hint: Differentiate…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: (i) By making the substitution o = tan 0, demonstrate the validity of %3D Parseval's theorem for…

A: Consider the function as ft=e-tdt

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…