u= - e' sinhx satisfies one of the f ollowing u = -u O"xx Not harmonic Harmonic u =u O "x

Q: Suppose thnat the tangent line to the graph or J is equal to the tangent line to e graph of g(r) =…

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Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of 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: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: Show that the functions have exactly one zero inthe given interval. r(θ) = θ + sin2 (θ/3) - 8, (-∞,…

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

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

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Q: |Calculate the indefinite integral / sec (0) tan(@)d0 using two different u-substitutions. Explain…

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Q: Find the derivative of f(2) = sinh(2²) – 2z cos(32). Is this an analytic functio %3D

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Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

Q: Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: lim 3 2y ソ→o ソーSiny -sin.

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Q: What is the minimum value of f(0) in the equation f(0) = 3 sin 40? %3D

A: To determine the minimum value of the below function. fθ=3sin4θ

Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

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Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

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…

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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: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

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

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

A: Consider the given function y=4cos0.5x

Q: When a particle is located a distance of x metres from the origin, a force of cos(x) Newtons acts…

A: The given question can be solved as shown in step2.

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

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: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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

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Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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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: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

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Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

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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: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy

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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 sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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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: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: limit x approaches zero, sin^2x/x

A: Given,

Q: Show complete solution. Determine the slope of the tangent line to the graph of the equation ey =…

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Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

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