Answers created by Steve M

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• How do you find ? a) the inverse g(x) of the function f(x)? b) graph f and g together? c) verify the derivative formula for f and g at the point c=2? {If f=x^3-1}
  
• If #f(x)=x^3-1# find the inverse #g(x)# of the function #f(x)#?
  
• Solve the following differential equation #y'= (2x)/((x-1)^2(x+2))#?
  
• Find arc length of #r=2\cos\theta# in the range #0\le\theta\le\pi#?
  
• A hole of radius r is bored through the center of a sphere of radius R. find the volume of the remaining portion of the sphere?
  
• What is the taylor series expansion for the tangent function (tanx)?
  
• Please help me with this calc question?
  
• How to solve #xy(dy/dx +1) = x^2 + y^2# by finding the general solution?
  
• How to do these question?
  
• How to derive power reducing formula for #int(sec^nx)dx# and #int (tan^nx)dx# for integration?
  
• How do you integrate #int 1/sqrt(e^(2x)+12e^x+35)dx#?
  
• Why the <x,y> vector field is different from <y,x> vector field?
  
• Question: Find the particular solution #y_p(x)# of homogeneous linear equation of the 2. order with constant coefficients. How do I solve it? Thank you! (pictures below)
  
• Question: find a general solution of homogeneous linear difference equation of the 2nd order with constant coefficients. How to solve it? Thank you. (pictures below)
  
• My question is: "find the particular solution y(x) of the given differential equation which complies with the initial condition" # xy'+x^2=2y# with #y(1)=0# How to solve it? Thank you!
  
• How to understand #y=f(2x)# ? Why is this really a compression? If #f(x) = 2x+3# can someone show a table for this? In my text book it says we divide the #x# value by #2#? I don't see why? Wouldn't we times it by #2#? Thanks.
  
• Hi everyone! My question is: "find the general solution y(x) of the given differential equation": #xy'+y=x^6# How do I solve this? Thank you for your answer!
  
• Double integrals: #int_0^1 int_(y-1)^(y-3) (x^2+2y) dxdy# ?
  
• #int_0^2 int_(y-1)^(y-3) (x^2+2y) dxdy# ?
  
• Can someone help me find the Maclaurin series for the given function?
  
• Dy/dx = y - 2x how to implicity differentiate?
  
• What is the solution of the Homogeneous Differential Equation? : #dy/dx = (x^2+y^2-xy)/x^2# with #y(1)=0#
  
• #y'' + 9y = 2x^2 - 5#, How about solution. (#y_h#=?, #y_p=#?)
  
• If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=x^2+5x+2#?
  
• What is an example of a quadratic equation with imaginary roots?
  
• Darivative of [{(sinx×sinx)+sinxcosx }/{(cosx×cosx)+sinxcosx}]=?
  
• What is the derivative of #f(x)= (2x-3)^3 (x+1)^2#?
  
• How do you find the distance travelled from t=0 to t=3 by a particle whose motion is given by the parametric equations #x=5t^2, y=t^3#?
  
• If #y= sinx/ x^2#, find #dy/dx# and #(d^2y)/(dx^2)#. Then prove that #x^2 (d^2y)/(dx^2) + 4x dy/dx + (x^2 + 2) y = 0# ?
  
• Solve #\int(e^(2x))/(1+e^(4x))dx#, OR #\intx\arcsin(x)dx# using infinite series?
  
• Can someone explain this?
  
• How do you use substitution to integrate #e^x * sin2xdx #?
  
• Find cot x and sec x give that sin x= 1/6 and cos x >0?
  
• How do you simplify #(4-5i)-(6-i)#?
  
• Find all the values of z (complex number) that satisfy the equality:? #z^2+|z|=0#
  
• Integrals Question With approximately what velocity does a diver enter the water after diving from a 30-m platform? (Use g=9.8m/sec). Thank you!!!
  
• What the slope of #x^4y^4=16# at #(2,1) #?
  
• If #u# and #v# are odd functions of #x#, what can be said about #(u+v)#,#(u-v)#,#(u/v)# and #u*v#? how do you find if they are Even, Odd or neither?
  
• What is a solution to the differential equation? : #dy/dx + (1-2x)/x^2*y = 1# when #y|_(x=1)=0#
  
• How to draw the region R whose area is given by the iterated integral. Then change the integration order and show that both orders give the same area? With step by step solution please?
  
• Given that #y= e^-x sinbx#, where #b# is a constant, show that # (d^2y)/(dx^2) + 2dy/dx + ( 1 + b^2) y = 0 # ?
  
• Show that if #y= (sin^-1 x)^2# then #(1 - x^2) (d^2y)/(dx^2) - xdy/dx - 2 = 0# ?
  
• How do you integrate #int x arcsec x # using integration by parts?
  
• Integrate the following (below) using infinite #\bb\text(SERIES)#?
  
• What is the general solution of the differential equation? : #(d^4y)/(dx^4) - 4 y = 0#
  
• Find the Riemann sum of f(x) = sinx on [-p,p]by using four subintervals of equal length and midpoint rule?
  
• I need to write 8i in polar form. how to find angle when 8/0 not defined ?
  
• Form a differential equation if #y=e^x#?
  
• Show that #y_1=x^2# is a solution to the differential equation #x^2y'' -(x^2+4x)y' +(2x+6)y=0 #?
  
• How do you integrate #int 1/sqrt(-e^(2x)-12e^x-37)dx#?
  
• Given the equation in picture below, what is? : a. #f'(x)# b. the derivative of #e^(f(x))#
  
• How do you evaluate the definite integral #inte^(lnx+2)# from #[1,2]#?
  
• How do you show that tan (θ) has period π in terms of a unit circle?
  
• How do you find the integral of #int 1/(t^2-9)^(1/2)dt# from 4 to 6?
  
• How do you integrate # (x^3+x^2+2x+1)/((x^2+1)(x^2+2))# using partial fractions?
  
• Given #f(x) = cosh(x+a/cosh(x+a/cosh( cdots)))# and #g(x)# its inverse, what is the minimum distance between then for #a > 0#?
  
• (a) Determine Δx and xi. Δx= xi= (b) Using the definition mentioned above, evaluate the integral. Value of integral ?
  
• How do you compute the 6th derivative of: #(cos(6x^2)-1)/(x^2) # at x=0 using a maclaurin series?
  
• How to determine the general solution to the system of differential equations ? #y'_1(t) = 9y_1(t) - y_2(t)# #y'_2 (t) = y_1(t) + 7y_2(t)#
  
• Can you please solve this in calculus? Thanks #y''''+2y'''+2y''+2y'+y=1/2cosx+xe^x#
  
• Prove the identity # sin theta/ (1-cos theta) - 1/sin theta -= 1/tan theta #?
  
• How do you write the complex number #(4-2i)(-3+i)# in standard form?
  
• How do you graph #y=-3 sec x#?
  
• What is a solution to the differential equation # xy' = y#?
  
• How to solve these questions steps by steps ?
  
• Find the Taylor series (check my work)?
  
• Inverse of #f(x)=(x^2+2)/(x-3)# ?
  
• State De Moivre's theorem and prove it for all integer values?
  
• Vectors - Span #RR^2#?
  
• A physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200 meter running track, how do find the dimensions that will make the area of the rectangular regions as large as possible?
  
• How do I find the greatest lower bound for the sequence #A={\frac{1}{n+10}}_{n=1}^{\infty}#?
  
• How do you find the points where the graph of the function # r=e^theta# has horizontal tangents and what is the equation?
  
• How to Use the rule of the appropriate chain and converting w to function of t before differentiating and then Express the answer in s and t?
  
• What is the derivative of #e^x sin(3^(1/2x))#?
  
• What does it mean if two vectors are orthogonal to each other?
  
• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=3x^2+2x+5# on the interval #[-1,1]# ?
  
• #x^3+24x-16# [0,4] verify mean value theorem?
  
• How do you solve #ln [((x+1) / x)]=1#?
  
• How do you use trig identities to show that this is true? #tan^3x/(1+tan^2x)+cot^3x/(1+cot^2x)=(1-2cos^2x sin^2x)/(sinxcosx)#
  
• How do you find the maclaurin series expansion of #1/(x+3)#?
  
• It is a vector question?
  
• How do you prove #(1+tan^2x)/(1-tan^2x)=1+tan2x.tanx# ?
  
• Evaluate: #int dx/(sin^2x+sin^2x*cos^2x+cos^2x)# ?
  
• How do you evaluate the definite integral #int dx/(1-x)# from #[-2,0]#?
  
• Setup the limit definition of definite integrals #int_-1^2(1+x^2)dx# ?
  
• What is the expected value of the sum of two rolls of a six sided die?
  
• .There was a proposal for the new size of the advisory boards to be placed at strategic locations along the expressway. The board must contain 50 square meters of print and margins of 4 meters at the top and bottom while 3 meters on each side.?
  
• Show #|f(b)-f(a)|<= |b-a|# ?
  
• Average of sin t *cos t how to find ?
  
• How do you find the length of the curve #y=(2x+1)^(3/2), 0<=x<=2#?
  
• Please explain?
  
• Calculate enough derivatives to guess the general formula for #f^((n))(x)#. And proof this by mathematical induction. #f(x) = 1/2-x# and #f(x) = cos(ax)#?
  
• What are the coordinates of the point of intersection of the tangents when the equation of the tangent to the curve #y= x^2 -6x + 5# at the points, #x = 1# and #x = 5# is/are found?
  
• The matrix ( w -9 4 w-12 ) , does not have an inverse. Calculate the value of w?
  
• How do you find the integer part of the following expresion?
  
• How do you integrate #int lnx/x^2# by integration by parts method?
  
• Nice question in calculas?
  
• What is f’(x) F(x)=cos(x)+3x^2+y ?
  
• How do you prove #(tanx+sinx)/(2tanx)=cos^2(x/2)#?
  
• Obtain a quadratic polynomial with following conditions?? 1. the sum of zeroes=1/3,the product of zeroes=1/2
  
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