Answers created by Ananda Dasgupta

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• How do you do this?
  
• How to find sum of the given series?
  
• What is the arc length of teh curve given by #r(t)=(2t , 2e^(-t) , e^(t) )# in the interval #t in [0,3]#?
  
• P(x^2)+x*q(x^3)+x^2*r(x^3)=(1+x+x^2)*s(x), p(1)=ks(1) and r(1)=kp(1). Then k=?????
  
• What is the net area between #f(x) = (x-2)^3 # and the x-axis over #x in [1, 5 ]#?
  
• Piece wise function sin(x-a)/(x-3), x not equal to 3 and other function equal b where x equals 3 . for what values of a and b function is continuous?
  
• Derivative of inverse of f(x)=e^(-2x)-9x^3+4 at point (0,5)?
  
• (d^4y)/(dx^4)+2d^3y/dx^3+(d^2y)/(dx^2)=cos6x??
  
• What is value of lim x tends to 0 [log (5+x) -log(5-x)]/ x. ?
  
• How do you use partial fraction decomposition to decompose the fraction to integrate #(z+1)/(z^2(z^2+4))#?
  
• How to calculate moment of inertia of a disc about its one diameter if given mass per unit area is proportional to distance from centre?
  
• #lim_(n -> oo) n^(1/n)=?# for #n in NN# ?
  
• If #sum_(i=1)^(n) cos(A_i) = n# then find #sum_(i=1)^(n) sin(A_i)#?
  
• What is lower Riemann sum?
  
• The question is below?
  
• Determine the kernel and range. HELP???
  
• Why is an ammeter connected in series in a circuit?
  
• How to find the coefficient of #x^50# in the expansion of the following?
  
• How do you integrate #6/(x^2-25)^2# using partial fractions?
  
• What is the arclength of #f(t) = (sqrt(t^2-t^3),t^3-t^2)# on #t in [-1,1]#?
  
• (2j×3i).k=? My text book says the answer is -6. But how?
  
• If ab + bc + ca is equal or greater than 2, what is the minimum possible value for a^2 + b^2 + c^2? This was on a noncalculator paper
  
• How do you resolve this integral?
  
• If #f′(x_0) = 5#, then #lim_{ℎ→0} (f(x_0+ℎ)−f(x_0−ℎ))/ℎ# ?
  
• If #hata_1,hata_2andhata_3 #are unit vectors and#2hata_1+2hata_2+hata_3=0# then angle between #hata_1 and hata_2 # is?
  
• What is the arclength of f(t)=(3t^2-1, 3t^3-t) on t∈[-1/sqrt(3),1/sqrt(3)]?
  
• If #hata_1+hata_2+hata_3=0# then the value of #|hata_1-hata_2|^2+|hata_2-hata_3|^2+|hata_3-hata_1|^2# is?
  
• How do you do 2/(1+x^2+y^2) integration?
  
• Solve the differential equation #y'=(y-x)^2#?
  
• Triangle A has an area of #18 # and two sides of lengths #5 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?
  
• Determine the relationship between the rates of change of f and g. ?
  
• Find two numbers whose sum is 12 such that the sum of the square of one plus 4 times the other is a maximum?
  
• Find the required limit algebrically, if it exists. lim (x+3)/(x-3) if x approaches 4 ?
  
• #lim_(x->-oo)(x*|__(1/x)__|)#?
  
• Two satellites #P_"1"# and #P_"2"# are revolving in orbits of radii #R# and #4R#. The ratio of maximum and minimum angular velocities of the line joining #P_"1"# and #P_"2"# is ??
  
• The answer ,please?
  
• If two objects are released from a certain height both will reach at the same time.but according to fluid dynamics (terminal velocity) the denser will reach first.does it mean that the concept of terminal velocity is wrong??
  
• How to find the velocity and acceleration at t=0?
  
• What is the equation of the tangent line of #f(x)=sqrt(x+1) # at #x=0#?
  
• Can someone help me find a and b if f(x) is continuous at π/2 , without using L'hospital rule? Please mention all formulae used too.
  
• A body is released from height equal to the radius of earth the velocity of the object when it strikes the surface is? 1) ✓gr 2) ✓2gr 3) 2✓gr
  
• What is the derivative of (x^x)^x?
  
• How do you solve #(11x - 5) ^ { 2} - ( 10x - 1) ^ { 2} - ( 3x - 20) ( 7x + 10) = 124#?
  
• Find value of | 368/21 #vec u# + 991/21 #vec v# - 1177/21 #vec w# | ?
  
• The ratio of two positive real numbers is #p+sqrt(p^2-q^2):p-sqrt(p^2-q^2)#then find their ratio of AM and GM?
  
• What are the equations of the tangent lines out P(2,1) to the parabola with equation #y = x^2#? Thank you!
  
• A student is investigating the effect on her wight when travelling in a lift. She is standing on scales which are graduated in Newtons.?
  
• How do you simplify #f(theta)=-tan4theta+sin2theta+cos4theta# to trigonometric functions of a unit #theta#?
  
• Use taylor series to evaluate #f^11 (0)# for #f(x) = x^3 cos(x^2)# ?
  
• For what angle range becomes double of height in a projectile motion?
  
• If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations then the combined harmonic mean....?
  
• If the AM and GM for 10 observations are both 15 then the value of harmonic mean......?
  
• What is the HM of 1,1/2,1/3.....1/n?
  
• How to solve this variable acceleration Q, parts a to c?
  
• How to integrate x^2/(x^3+1)?
  
• If a fair coin is flipped #5# times, what is the probability that there will be at least #3# tails?
  
• How to find net capacitance?
  
• #f(2)=f(4)=g'(2)=g'(4)=2# and #g(2)=g(4)=f'(2)=f'(4)#. If #h(x)=f(g(x))#, then #h'(2)#?
  
• How do you prove #sin(x+y)# = #(tanx+tany)/(secxsecy)# ?
  
• How to use rolles theorem for #f(x)= (x^3/3)- 3x# on the interval [-3,3]?
  
• Find the area bounded by the curve y=e^(x/3) , the tangent line which is y=1/3 e^(3)x - 2e^3 and the x-axis?
  
• How to solve #x^3-3x-2=0# ?
  
• If #sin2x=0 ⇔ x=(kpi)/2#, why isn't #sin5x=0 ⇔ x=(kpi)/5#?
  
• The answer should be ?
  
• What is the slope of the tangent line of #(y/x)e^(x/y-x^2)= C #, where C is an arbitrary constant, at #(1,2)#?
  
• The Earth takes 1 day to rotate once about its axis. What is the angular velocity of a point on the surface of the Earth?
  
• How do you evaluate the integral #int sqrtxsqrt(4-x)#?
  
• A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to maximize and minimize the total area?
  
• Why does light get polarised when reflected and refracted?
  
• How to differentiate #y= (ln(4x^2))/(3^(6x)# ?
  
• Did I do this First order linear differential equation right?
  
• Three rods each of mass M and length L, are joined together to form an equilateral triangle. What is the moment of inertia of a system about an Axis passing through its centre of mass and perpendicular to the plane of the triangle?
  
• How to check work for First Order Linear Differential Equation?
  
• S is a geometric sequence? a)Given that (#sqrtx#-1), 1 and (#sqrtx#+1) are the 1st 3 terms of S, find the value of #x#. b)Show that the 5th term of S is 7+5#sqrt2#
  
• How to determine the depth of a water well given the initial velocity, the time and the speed of sound?
  
• The lengths of the sides of a traingle are 14 and 16. which of the following is a possible value of the perimeter of the given triangle?
  
• Compute this integral #int_(3^(1/2))^(35^(1/2))(x^2+1)^(1/2)/xdx#?
  
• If #alpha# and #beta# be the value of #x# obtained from the equation #m^2(x^2-x)+2mx+3=0# and if #m_1# and m2 be the two value of m for which alpha and beta are connected by the relation alpha by beta +beta by alpha =4/3 find the value of m1^2/m2+m2^2/m1?
  
• W= |u| * v +|v| * u Where u and v and w are all non-zero vectors Show that w bisects the angle between u and v ?
  
• A box without a top is made from a rectangular piece of cardboard, with dimensions 27 centimeters by 18 centimeters, by cutting out square corners with side length x centimeters. Which expression represents the volume of the box in terms of x?
  
• In △XYZ , m∠X=38∘ , m∠Z=67∘ , and YZ=25 feet . What is XZ ? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
  
• Find Fxx of the following equation?
  
• Find arc length of #r=2\cos\theta# in the range #0\le\theta\le\pi#?
  
• If the mass of earth were 2 times the present mass,the mass of the moon were half the present mass and the moon were revolving round the earth at the earth at the same present distance, the time period of revolution of the moon would be(in days)?
  
• In a series RC circuit, does the phase difference between the capacitor and the resistor voltages depend on the values of R and C?
  
• What is the solution set of the equation #3x^5 - 48x = 0#?
  
• How can I use Kepler's law of harmonies to predict the time Mars takes to orbit the sun?
  
• How to find the moment of inertia of a cut-out object?
  
• How do you compute the 200th derivative of #f(x)=sin(2x)#?
  
• Prove It? Sin3θ/Sinθ-cos3θ/cosθ=2
  
• Please solve q 85 ?
  
• How to know that the poles of #sinz/{zcosz}# at 0,+π/2 &-π/2 are simple poles?
  
• Finding whether the following integral converges or diverges?
  
• How could I prove this? Would this be using a theorem from real analysis?
  
• Calc 2 questions super lost! Evaluate a power series to find the sum of the series, or show that the series diverges. (If a series diverges, enter DIVERGES.)? (a) #11/1-11/3+11/5-11/7+11/9-11/11+....# (b)#sum_(n=2)^oo ((-1)^n(8^n))/(n!) #
  
• How do you find the area under the graph of #f(x)=e^(-2lnx)# on the interval [1, 2]?
  
• How to differentiate this function to find f'(7)?
  
• How do you show the convergence of the series #(n!)/(n^n)# from n=1 to infinity??
  
• How do you solve this question?
  
• Six identical particles each of mass ‘m’ are arranged at the corners of a regular hexagon of side length ‘L’. If the masses of any two adjacent particles are doubled. The shift in the centre of mass is???
  
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