part 1 of 3 (i) Express the improper integral S 3xe-x/2 dx I = as lim It with each It a proper integral. t→∞

Q: sin'y 11) lim y--TT 1+cosy •TE1+cosy

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Q: Express the limit as a definite integral: limn→∞ sec² (1) ΣΩ .) π k=0 4n Of sec(πx) dx O T O Sot…

A: To express the following limit as a definite integral.

Q: Show that y = sin (1/x) has no limit as x approaches zero from either side

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Q: For-1 <x < 1 let arcsin(x) f(z) = %3D Find the antiderivative F(x) of f(x) such that F(0) = 1.

A: We use substitution substitution method to find anti derivative

Q: Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Asume that h(x,…

A: Sol

Q: Average Cost Jesaki Water Sports incurs the following costs in producing a water ski vests in one…

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Q: If u'(x) between u(x) and v(x). v(x), write a statement involving integral sign giving the…

A: Given: u'(x)=v(x)we know that u'(x)=du(x)dxdu(x)dx=v(x)du(x)=v(x) dx

Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: Inx dr Lim их 3.

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Q: du u (х, 0) — и(0,0) lim x→0 %| да (0,0)

A: Consider a function f(z)=u(x,y)+iv(x,y) such that     z=x+iy∆z=∆x+i∆y If the function is…

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

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Q: x² sin x (x, y) (0,0) x² + y² Determine whether lim exists.

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Q: ¡CON(I) 1 G(r): = -T₁₂ -2 dy 1-y³

A: Gx=∫x-2cosx11-y3dy To Find: Evaluate the above definite integral Using the Fundamental Theorem of…

Q: rt01+sin x +00 -dx x2

A: Here we will use  integration by parts  ∫uv dx= u ∫v dx -∫dudx∫vdxdx

Q: Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer…

A: The given functions, 1. y=tanx6 2. y=x5+9 3. y=e7x We have to write the functions in composite form…

Q: Use integration by parts to evaluate lim Sest f(1)dt. (Let u = Z→∞J f(t) and dv = est dt.)

A: As per the question we are given a limit of an integral, and we have to use the integration by parts…

Q: tan(1 – x) limx→1 2 2x +x – 3,

A: Limit

Q: Consider the function f(x) = x ² + 3. Part 1: Compute the slope of the the tangent line to y = x2 +…

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Q: * sec(x) tan(r) de.

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Q: 3 dx

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Q: Theatem: Let fixy be afunction e If { VicY :jEI} is a callection of subsets of y then jeJ JET JEJ

A: Given:f:x→y be a function We need to prove (i)f-1∪j=1∞Yj=∪j=1∞f-1Yj (ii)f-1∩j=1∞Yj=∩j=1∞f-1Yj…

Q: please show where the absolute stripes of " ln|y-1| " go?

A: Consider the differential equation , , where .The solution is .Also observe that thegeneral solution…

Q: Find lim R→∞ -R ex/6 e + 1 dx using the rectangular contour (explain in detail)

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Q: 4 + cos t -dt 1 – sin t

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Q: Find lim (x,y) → (0,0) 4e4y sin (2x) X 4e4y sin (2x) X lim (x,y) →(0,0) (Type an exact answer.) =

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Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)

Q: f sint dt Evaluate lim

A: We will use DL hospital rule and Newton leibniz formula to solve this question.

Q: x+y %3D 21. Prove that tan-x + tan-'y tan - xy.

A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

Q: Show that arcsech(x) = arctanh(√1-x²) where arcsech(x) is the inverse of f: [0, ∞) → R, f(x) =…

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Q: lim t→0 4t² + 3t sin t +2

A: To evaluate the following limit.