2. The period of the function f(x) = tan(3r) is 27 i) 3 iii) iv) 27 v) not listed

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: 14. ry = coS

A: Given:      xy=cos-1xy+1        y=cos-1xy+1x differentiating on both sides     dydx=ddxcos-1xy+1x…

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

A:

Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

Q: Find the period of the function f(x) = sin(1.05x).  Provide 4 decimal places.

A:

Q: Find the period of the function f(x) = cos(0.10x+2.07).  Provide four decimal places.

A:

Q: on of period 2 pi in t. (x+sin r)(x

A: The differential equation is given as, dxdt=x+sin2tx-esint Let x=ft be the solution of the…

Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

A:

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

A:

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: 8. What is the period for this relation y = cos(4x)

A:

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

A:

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

A:

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

A:

Q: If f(x,y,z)=In(x²y+sin² 12

A:

Q: 19. Find the points of inflection on the graph of f(x) = x+2 cosx on the interval [0, 27].

A:

Q: (a) Show that cos(x²) > cos x for 0 ;. 1

A:

Q: - cos(x) - 1, choose all values of c in the interval (, 5 For f(x) guaranteed to exist by Rolle's…

A: For fx=-cosx-1, choose all the values of c in the interval π2,5π2guaranteed to exist by Rolls's…

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

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

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

A:

Q: The domain of y = cos x is. range is and the %3D

A: It is known that cosx≤1 for all x∈ℝ.

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: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

A:

Q: 5. The function f(0) = (sin O+cos 0) + (sin 0– cos 0) may be written as

A:

Q: Find the absolute extrema of the function on the closed interval.

A: The given function is y=tanπx8    on  0, 2. Compute the critical points as follows.…

Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

A:

Q: Find the egetion of the tanqent line on the interval (o,5) to co.1, 6.2)

A:

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

A:

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

A: Hence linear independent

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: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

A:

Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: on [ 0, 2î] ,determine all velafive the Finction. .If f(x) = sin x t cos X extrema for

A:

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

A:

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

A:

Q: is The period of the function f(x) = 3sin4 (x-) (1); TE (c) (a) 2 3

A: Given f(x)=3sin4(x-π4)We know that y=A sin(B(x+c))+DFrom the equation A is amplitudePeriod is 2πBC…

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

A:

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: If f(x)= (A) B D plans √ 1+1² tanx I+e' f sec ³x tanx 1+tan²x Itefan 1+e -dt, then f'(x) equals…

A:

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A: