Compute : exp(i sin(e¬ni)).

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: Let csct = V5,t e QII Find sin(2t) 4 O 2 V5 V5 25

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Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

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Q: Find the arclength of y = 2a/2 on 1 <a< 2

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Q: Find the x+ iy form of tan(i), arctan(2i), and tanh(i 3º5).

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Q: az -? Since it is du coSV.y=. av ) z = In (xry*),x = e"cosv.y= e"sinvr

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Q: | cos r In(sin z)dr

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Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

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: Find the maclauin's sesies for y= cos(%)

A: y=fx=cosx2 Differentiating with respect to x, we get f'x=-12sinx2 Again differentiating with respect…

Q: D cos( 5t D sinf see Dcost cast) 4

A: See the attachment

Q: Transform F(s) (giving you cos 5t + t³

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Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: let X ~ P()find the third central moment.

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Q: = cos(x + y), when x = 0, y = " %3D

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Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: Find the arclength of y = 6x – 3 on 0 < x < 4. Give the exact answer. -

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Q: Write the DE, e" y' + e2y= sin a in the general form.

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: S sec" (0) tan" (0) do is u = tan(0)

A: Evaluate ∫sec10θ tan8θ dθ

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: | cos xdx sin x

A: Given query is to find the solution o the integral using substitution.

Q: Sketch the curve corresponding to r = 1 + cos θ.

A: we have to sketch the graph of the polar curve r=1+cos θ.

Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

Q: Find the velocity and acceleration of a particle whose position function is <(1)=sin(21)+ cos(t)

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Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: cos(x) dx

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Q: Find d cos Z dz

A: Use the properties of differentiation and the derivative formula ddxeax=aeax, to calculate ddzcosz,…

Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: Find the arclength of y 4x? + 4 on 0 < x < 2

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Q: Integrate the right side. cos u du + C 187

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Q: Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z…

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Q: Calculate us (t) * sin(t) using the definition of the convolution

A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

Q: Use Green's theorem to evaluate $y – sinx)dx + cosx dy Where c the triangle of the adjoining figure…

A: Green`s Theorem:-  Green`s Theorem states that the line integral is equal to the double integral of…

Q: @lProve f A=3i+ rotating an ang

A: we have to prove that the length of the vector 3i+2j+k does not change when rotating the axes around…

Q: . Consider the function f(x) = cos(0.6z). %3D i. For the argument of cosine, 0.67. to vary by 2T,…

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Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: Let glt) =e"t + Ž G ). sinCnt) Slre y'+4y=gGt),( deare the anouerr こ as a pariès.)

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Q: "ind the orthogonal compliment to S = span{

A: Here we have to find the,

Q: T= 8 cos 30. with /met: A =

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Q: Consider that sin(x) = e, where %3D 0<x< T, then dy tan (x) dx False O TrueO

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.