3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to evaluate J sec"x dx.

Q: Use first principle rule and prove that: dy\dx = secx tanx If, y=sec(x) Then y' = sec(x)tan(x)

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Q: Evaluate (int) tan^4 t sec^4 t dt

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Q: sec 3x tan² 3x dx

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Q: integral -{cay,a> 91-) Evoluate te nplhas)ss - 24x<0, Ocyc1, -16241} . where

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Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: tan 44.1°

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Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: find integral tan 5 x sec 7 x dx

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Q: Suppose a particle has velocity given by v(t)=sin(t). What is the net displacement of the particle…

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Q: 2 9) -sinh? -cosh -dz

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Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

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Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

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

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Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: Q. Use first principle rule and proue that secn tene if y = secx %3D

A: Note  your Question is wrong because right Question is  y=sec(x) then y' = sec(x)tan(x)

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

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

A: GivenZ=sinhyx

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

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: 2. An explosion is recorded by two microphones that are 2 miles apart. Microphone M, received the…

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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: 4. A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height…

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Q: What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

A: We need to compute the length of the arc of the given curve over the interval [3,6]

Q: (a) Show that tan x = dx sec?x using quotient rule.

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Q: d Use quotient rule to prove [cscx] = -cscxcotx. dx

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Q: What is the integrable form of sin-cos-sino de? 2 (A -2 | sinu du B / Ju?- 1 du 2 /1-u² du D cosu du

A: Given: ∫sin θ2 cos θ2sin θ dθ Find the integral form of the given function. By using trigonometric…

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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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: Which formula gives the x-coordinates of the maximum values for y = cos(x)?

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Q: sec (7x)tan' (7х)dx

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Q: Q. Use first principle rule and proue that secx tanl y = secx

A: Given : y=secx To prove : dydx=secxtanx using first principle. Proof : By First principle, we have…

Q: (1+ tan(z)) sec² (x) dx

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Q: I* cos z lim 1³+2

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

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: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

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

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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: Give exomple of o line ar equation s unknown

A: First we see the defination of linear equation then give the answer.

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: =sec (Xty)

A: dydx=secx+y  Let v=x+y  1+dydx=dvdx  dydx=dvdx-1  dvdx-1=secv dvdx=secv+1 dvsecv+1=dx