B.Sc. Differential Calculus (B.Sc.) (B.Sc notes)
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(B.Sc notes)
1
if y=e^a.sin(x) find (yn)0
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2
if u=(x+y)/(1-xy) and v=tan-1(x)+tan (y) find jacobian of u;v with respect to x and y.Are they depen
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3
if Y={sin(x)}^2.{cos(x)}^3;find Yn
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4
Nth derivative of x/(x^2+a^2)
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5
Find n th derivatives of 1/(x^2+a^2)
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6
if In=d^n/dx^n (x^n.logx) then prove thatIn=n! (logx+1+1/2+1/3+.....+1/n)
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7
If Φ be the angle between the tangent To the curve and radius vector tanΦ=(xdy/dx-y) /(x+ydy/dx)
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8
B.Sc.Mathematics:Pedal formula for Radius of curvature
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9
Find the radius of curvature of curve p^2=a*r
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10
Find the pedal equation of curve r=a.e^θ.cotα
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11
B.Sc. Mathematics:Find the pedal equation of cardiod r=a(1+cosθ).
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12
(p1)^-2/3 +( p2)^ =(L)^-2/3be the radii of curvature at the extremities of focal chord of parabola
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13
Envelope equation of xcos^n (t)+y.sin^n (t)=c
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14
Find radius of curvature at (r,θ) of curve r=a.cosθ
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15
Continuity is necessary but not sufficient condition for differenciability
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16
Find envelope of family of lines y=am+a/m
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17
Differentiation of x^2n by two different method and show that1+n^2/1^2+n^2 (n-1)^2/1^2.2^2+...=!2n/
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18
If u=x^2+v^2+w^2;v=x+y+z;w=xy+yz+zx;show that jacobian of u,v and w with respect to x,y ,z;find rela
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19
Find the radius of curvature for the pedal curve r=f (r)
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20
B.Sc. Mathematics :radius of curvature for the curve r=a (1-cosθ)and show that p^2/r is constant.
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21
Expansion of cos (x-π/4)
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22
Maclaurin Theorem State and Proof
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23
Prove that the function f(x,y)=x^2-2xy+y^2+x^3-y^3+x5 have neither maxima nor minima at origin.
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24
Curve tracing in cartisian form:symmetry (General rule)part1/7
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25
Find the Cartesian form of radius of curvature of a curve
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26
If u=f (x,y) where x=rcosθ,y=rsinθ then prove....partial differentiation of
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27
If u=f (x,y) where x=rcosθ,y=rsinθ then prove....partial differentiation of
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28
differentiate log (x^2+y^2) partially w.r.t.x by first principle
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29
Find Yn if Y=1/x^4-a^4
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30
If y=x^n.logx ,prove that yn=n!(logx+1+1/2+1/3+.......+1/n)
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31
Taylor's theorem for real function
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32
If f (x)=x^2.sin (1/x),x =/0 and f (0)=0 prove f (x)is diffgerentiabl on every point and f'(x)is no
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33
part -3 कुरान और साँइसIron miracle part3
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34
B.Sc. Mathematics :Differential Calculus;Limit:If lim f (x) exist at x=a,then it is unique.
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35
B.Sc. Mathematics :Find the value of the limits limit e^(-1/x)
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36
If y^1/m+y^-1/m=2x prove that(x^2-1)yn+2+(2n+1)xyn+1+(n^2-m^2)=0 ||Top Math Channel||
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37
A limit problem (IIT-JEE ); B.Sc. math open universities
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38
B.Sc. math: Find condition that the conic ax^2+by^2=1 and a1x^2+b1y^2=1 should cut orthogonally
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39
B.Sc. Mathematics :Arithmetical Definition of Continuity
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40
B.Sc. Mathematics :Kind of discontinuity
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41
B.Sc. Math:show that f(x)=x.sin (1/x) when x does not equal to zero and f (x)=0 is continuous at x=0
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42
B Sc.Mathematics:A problem of limit(Hospital rule)
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43
Discuss the maximum or minimum values of u whereu=2a^2.x.y-3ax^2.y-a.y^3+x^3.y+x.y^3
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44
Discuss the maximum or minimum values of u where u=2a^2.x.y-3ax^2.y-ay^3+x^.3y+x^3.y+x.y^3
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45
If u=sin-1(x/y)+tan-1(y/x);show that x.del u/del x+y.del u/del y=0
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46
If f(x)=e^(-1/x),show that at x=0, the right hand limit is zero while the left hand limit is infinit
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47
If y1=r.sinθ1.sinθ2 y2=r.sinθ1.cosθ2 y3=r.cosθ1.sinθ3 y4=r.cosθ1.cosθ3 Find the value of J(y1,y2,y3,
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48
What should be the value of n in the equation to the curve y=a^(1-n) x^n in order that the subnormal
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49
Expand e^a.cos-1(x) by Maclaurin Theorem
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50
Expand e^(x+h) by Taylor's theorem
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51
If ax^2+by^2+cz^2=1 and lx+my+nz=0 find the values of dy/dx and dz/dx.
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52
If ax^2+by^2+cz^2=1 and lx+my+nz=0 find the values of dy/dx and dz/dx.
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53
If ax^2+by^2+cz^2=1 and lx+my+nz=0 find the values of dy/dx and dz/dx.
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54
If ax^2+by^2+cz^2=1 and lx+my+nz=0 find the values of dy/dx and dz/dx.
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55
If f(x)=x^n;prove that f(1)+f'(1)/1!+f''(1)/2!+...+f^(n)(1)/n!+...=2^n
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56
Find radius of curvature of curve x^2.y=a(x^2+y^2)
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57
n'th derivative of x/(x^2-a^2) B.Sc.Mathematics Calculus:Successive Differentiation:
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58
Find n th derivative of 1/6x^2+11x+9=0
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59
If y=tan-1(x) ;find yn
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60
To prove sin(ϕ)=rd/dr and cos(ϕ)=dr/ds
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61
Use Taylor's theorem to prove that tan-1(x+h)=tan-1x+h.sinθ.sinθ/1-(hsinθ)^2.sin2θ/2
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62
Find yn ;if y=x^n/1+x
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63
Find value of 'c' of Lagrange's MVT if f(x)=x.(x-1)(x-2);a=0,b=1/2
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64
A particle describes the curve lemniscate of Bernoulli under a force F to pole.Find the law force
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65
Expand tan(x) in terms of (x-pi/4)
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66
LEIBNITZ'S THEOREM proof in Hindi/Urdu
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67
If the normal at any point to the curve x^2/3+y^2/3=a^2/3 makes angle phi with x-axis ,show that its
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68
part- 2 iron miracle of quran
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69
#25December Jesus Christ in holy Quran(Miracle of Quran)
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70
State ε-δ definition of limit of a function use the definition to lim(2x+3)=5 at x=1
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71
Trace the curve y=x^3
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72
If u=dy/√(1+x²+y²),prove that d²u/dxdy=d²u/dydx,all partial differentiation
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73
Verify that del^2z/delxdely=del^2z/delydelx when z=x^y+y^x
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74
Find the asymptotes of the curve (x-2y)^2(x-y)-4y(x-2y)-(8x+7y)=0
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75
Find the point of inflection on the curve (θ^2-1)r=aθ^2
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76
Find the envelopes of the lines x/a+y/b=1,where a and b are parameters related by a+b=c
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77
Find the asymptotes of the following curve: x^4-x^2y^2+x^2+y^2-a^2=0
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78
Find first partial derivatives, second order partial derivatives and cross derivatives of following
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79
Verify Rolle's theorem for the following function:f(x)=2x^3+x^2-4x-2
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80
Find the asymptotes of the following function:y^3+x^2y+x^2y-y+1=0
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81
If u=x^2-y^2,v=2xy,x=rcosθ,y=rsinθ. find del(u,v)/del(r,θ), Jacobian of u ,v with respect to x,y.
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82
Prove that if p be the radius of curvature at any point P on the parabola y^2=4ax and S be its focus
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83
Find the first and second partial derivatives of z=x^3+y^3-3axy
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84
Find the nth derivative of 1/x^2+a^2
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85
Find the asymptotes. of the curve x^3+2x^2y+xy^2-x^2-xy+2=0.
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86
Solve:. y=ptanp+logcosp
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87
Expand function x^2+3y-2 in terms of (x-1) and (y+2) by using Taylor's theorem
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88
Find the radius of curvature of cardioid s=8asin^2(xi/6)
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89
Find Nth derivative of tan-1(x/a) or D^n(tan-1x/a)
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90
If cos-1(y/b)=log(x/n)^n, prove that x^2yn+2+(2n+1)xyn+1+2n^2yn=0
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91
If y=[x+√1+x^2]^m,show that (1+x^2)y2+xy1-m^2y=0 hence prove that (1+x^2)yn+2+(2n+1)xyn+1+(n^2-m^2)y
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92
Rolle's theorem statement and proof
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93
If x=c.cosu.coshv,y=c.sinu.sinhv,prove that del(x,y)/del(u,v).
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94
If f(x)=(x-1)(x-2)(x-3) and a=0,b=4.Find 'c' of Lagrange's M.V.T
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95
Expand logsinx in power of (x-2)
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96
Geometrical interpretation of Rolle's Theorem
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97
Verify Rolle's theorem for the following function:f(x)=10x-x^2.
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98
If u=logtan(y/x)
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99
If x^xy^yz^z=c, show that at x=y=z,del^2z/delxdely=[xlog(ex)]^-1
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100
If x^y+y^z=a^b ,find dy/dx. #partial_differentiation
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101
If x=u(1+v) and y=v(1+u) ,find the Jacobian of x,y with respect to u,v. #jacobian
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102
Show that in the equiangular spiral r=ae^θcotα,,the tangent is inclined at a constant angle α to the
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103
f(x)=(√2cosx-1)/(cotx-1),x≠π/4,f(x)=α,x=π/4,what should be the value of α for which f(x) is continuo
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104
Expand sec-1(x+h) in ascending power of h by use of Taylor's series.
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105
(Reharsal video) Miracle of Quran.For Dawah purpose
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106
Find the radius of curvature at any point of the ellipse p^2=a^2cos^2Ψ+b^2sin^2Ψ.
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107
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108
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109
If y=(logx)/x; then prove that yn=(-1)^n/x^n+1!n[logx-1-1/2-1/3-.........-1/n]
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110
Find the n th derivative of xtan-1x. Find D^n[xtan-1x] or d^n(,xtan-1x)/dx^n
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111
Determine the maximum and minimum of x^3+y^3-63(x+y)+12xy .Find the maximum and minimum.
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112
Find the Cartesian equation of curve x=acos^3t , y=bsin^3t (in parametric form)
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