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# Important Questions for BE Printing and Packaging Technology Semester 1 (FE First Year) - University of Mumbai - Applied Mathematics 1

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Applied Mathematics 1
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"If"  x=uv & y=u/v "prove that"  jj^1=1

Appears in 2 question papers
Chapter:  Complex Numbers
Concept: .Circular Functions of Complex Number

Prove that sin^(-1)(cosec  theta)=pi/2+i.log(cot  theta/2)

Appears in 2 question papers
Chapter:  Complex Numbers
Concept: Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ

Prove that 𝒕𝒂𝒏𝒉−𝟏(𝒔𝒊𝒏 𝜽) = 𝒄𝒐𝒔𝒉−𝟏(𝒔𝒆𝒄 𝜽)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: .Circular Functions of Complex Number

If cos alpha cos beta=x/2, sinalpha sinbeta=y/2, prove that:

sec(alpha -ibeta)+sec(alpha-ibeta)=(4x)/(x^2-y^2)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

Prove that the matrix 1/sqrt3  [[ 1,1+i1],[1-i,-1]] is unitary.

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: .Circular Functions of Complex Number

If z =log(e^x+e^y) "show that rt" - s^2 = 0  "where r"= (del^2z)/(delx^2),t=(del^2z)/(dely^2)"s"=(del^2z)/(delx dely)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

If Z=tan^1 (x/y), where x=2t, y=1-t^2, "prove that" d_z/d_t=2/(1+t^2).

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

Find the nth derivative of cos 5x.cos 3x.cos x.

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

Evaluate : Lim_(x→0) (x)^(1/(1-x))

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

If x = uv, y =(u+v)/(u-v).find (del(u,v))/(del(x,y)).

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

Find all values of (1+i)^(1/3) & show that their continued
Product is (1+i).

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: D’Moivre’S Theorem

If y=2^xsin^2x cosx find y_n

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

If u=f((y-x)/(xy),(z-x)/(xz)),"show that"  x^2 (del_u)/(del_x)+y^2 (del_u)/(del_y)+x^2 del_u/del_z=0

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: .Circular Functions of Complex Number

Show that the roots of x5 =1 can be written as 1, alpha^1,alpha^2,alpha^3,alpha^4 .hence show that (1-alpha^1) (1-alpha^2) (1-alpha^3)(1-alpha^4)=5.

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Powers and Roots of Trigonometric Functions

If u=x^2+y^2+z^2 where x=e^t, y=e^tsint,z=e^tcost

Prove that (du)/(dt)=4e^(2t)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Review of Complex Numbers‐Algebra of Complex Number

Expand 2x^3+7x^2+x-6 in powers of (x-2)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Expansion of sinnθ, cosnθ in powers of sinθ, cosθ

Using De Moivre’s theorem prove that]

cos^6theta-sin^6theta=1/16(cos6theta+15cos2theta)

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: D’Moivre’S Theorem

If tan(x/2)=tanh(u/2),"show that" u = log[(tan(pi/4+x/2))]

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Inverse Hyperbolic Functions

Solve  x^4-x^3+x^2-x+1=0.

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: D’Moivre’S Theorem

Show that all roots of (x+1)^6+(x-1)^6=0 are given by -icot((2k+1)n)/12where k=0,1,2,3,4,5.

Appears in 1 question paper
Chapter:  Complex Numbers
Concept: Powers and Roots of Trigonometric Functions
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