b) u = ti + cos t j + sin t k and v = i – sin t j + cos tk.

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

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Q: To compute sin (3t) cos" (3t) dt, first you need to I Select) * then subsitute u = [ Select ) * and…

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Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: When a particle is located a distance meters from the origin,a force of Cos(πx/3) newtons acts on…

A:

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

A: Given information is :

Q: What is the integrable form of sin-cos-sin@ de? 2 2 sinu du cosu du

A:

Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: a) Differentiate f(x) = sin x from first principtes. %3D

A:

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: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

A:

Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: A particle that is located x meters from the origin is subject to a force of 10 sin² () in Newtons.…

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Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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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: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

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: cos ve J Vē sin? ve de = 2 sin ve 1 jus O 2 + c sin ve

A: Given ∫(cos(√θ)/√θsin2√θ)dθ   Let √θ= t     Integrate on both sides     (1/2√θ)dθ= dt            dθ=…

Q: The force on a particle is described by 4x +1 at a point x along the -axis. Find the work done in…

A: Given  Force F = 4x3+1

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: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: A boy is pushing a box with a force that can be described by the function: (x) = x³ — sin 2x + 1,…

A: We have to use integral to find work done

Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

A:

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

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Q: When a particle is located a distance meters from the origin,a force of cos  ( pie x / 3 )newtons…

A: Given: To find the work done by a particle when moving from x = 1 to x = 2, the formula is given…

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

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

A:

Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: What is the integrable form of sin-cos-sine de? 2 2 (A) - - B -2 sinu du (D cosu du

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: show that1) d/dz [cosz] = -sin z

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Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

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Q: Teorema de residuos: muestre que z=0 es un cero de orden 2 de 1-cos(z)

A: To show that z=0 is the zero of order 2 of the function  fz=1-cosz

Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

A:

Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2>0 then…

Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

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Q: cos' x dx

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Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

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

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Q: Integrate the trig identity 2 cos j x cos kx = cos(j + k )x + cos(j -k )x to show that cos j x is…

A: