Answers created by Tom

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• For a spontaneous process in an isolated system, the change in entropy is positive. Why? Why not?
  
• Question #44d55
  
• Question #d453a
  
• Question #49458
  
• What is the equation of the tangent line of #f(x) =x^2-sqrt((3x^2-9x)/(x+6))# at # x = 3#?
  
• How do you find the derivative of #y=ln(cosx^2)#?
  
• Four times a number is 6 more than the number. What is the number?
  
• How do you find the integral of #sin(2x)cos^2(2x)dx#?
  
• How do you differentiate #f(x)=(x^3-2x)(e^x-x^2)# using the product rule?
  
• How do you integrate #1/(s+1)^2 # using partial fractions?
  
• How do you differentiate #ycosx^2-y^2=y/x^2#?
  
• How do you find the integral of # 1/sin^2(x)#?
  
• How do you use the definition of a derivative to find the derivative of #f(x) =e^x#?
  
• How do you find the derivative of the function: #arccos(x^2)#?
  
• How would you simplify #sqrt2*sqrt10#?
  
• How do you integrate #int 1/sqrt(4x+8sqrtx-3) # using trigonometric substitution?
  
• How do you integrate #int 1/sqrt(e^(2x)-2e^x+10)dx# using trigonometric substitution?
  
• Can you integrate #int e^(-x^2 # using integration by parts?
  
• Does #a_n=x^n/(n!) # converge for any x?
  
• Please find the value for this integration. What is the answer?
  
• How do you find the determinant of #((0, 1, 2, 3), (0, 0, 2, 0), (3, 10, 12, 20), (0, 0, 0, 4))#?
  
• What does #arcsin(cos ((-pi)/3)) # equal?
  
• How do you use the ratio test to test the convergence of the series #∑ ((4n+3)^n) / ((n+7)^(2n))# from n=1 to infinity?
  
• Question #cd57a
  
• How do you solve #3^(x-2)=13^(4x)#?
  
• How do you find the exact value of #cos[arctan(-8/15)]#?
  
• How do alkyl groups affect acidity?
  
• What is the use of iso, sec & tert in IUPAC naming of organic compounds?
  
• How do you factor #y=4x^3+12x^2-16x-48 #?
  
• How do you integrate #int x sin sqrtx dx # using integration by parts?
  
• How do you integrate #int x /sqrt( 16 - x^4 )dx# using trigonometric substitution?
  
• How do you integrate #int x^3*sqrt(4+x^2) # using integration by parts?
  
• How do you evaluate the integral of #int (sin^4x)dx#?
  
• Question #25bda
  
• How do you integrate #int 1/sqrt(e^(2x)+12e^x-45)dx# using trigonometric substitution?
  
• Question #7a7ca
  
• How do you solve #(3x+2)/(3x-2)=(4x-7)/(4x+7)#?
  
• How do you find all the real and complex roots of #z^5 =1#?
  
• How do you find the inverse of #y=log_(1/2) x#?
  
• If #f(x) = sin x#, what is #f''(pi/6)#?
  
• What is #int_0^pi sin^2(lnx)#?
  
• What is the equation of the line passing through #(48,7)# and #(93,84)#?
  
• How do you integrate #int 1/sqrt(3x^2-12x-5)dx# using trigonometric substitution?
  
• How do you find the horizontal asymptote for #b(x)= (x^3-x+1)/(2x^4+x^3-x^2-1)#?
  
• What is the instantaneous velocity of an object with position at time t equal to # f(t)= (tsqrt(t+2),t^2-2t) # at # t=1 #?
  
• What is the equation of the line perpendicular to #y=-9/7x # that passes through # (3,7) #?
  
• Question #047be
  
• What is the slope of any line perpendicular to the line passing through #(3,12)# and #(-5,17)#?
  
• If #H(x)=6ln(x^2-5)+3ln(4)#, what is #H^-1(x)#?
  
• How do you change #10z^12# into polar coordinates where #z = 2 +4i#?
  
• What is the equation of the normal line of #f(x)= x+x/(1+x/(1+1/x))# at #x = 1#?
  
• What is #x# in #4^(2x+5) = 5^(2-x)#?
  
• What is the arclength of #((e^tlnt)/t,t/(e^tlnt))# on #t in [2,4]#?
  
• How do I find the direction angle of vector #<1, -sqrt3>#?
  
• How to integrate ?
  
• How do you write the partial fraction decomposition of the rational expression # (x^3-x^2+1) / (x^4-x^3)#?
  
• How do you integrate #int ( x^2 + 2 ) / (x+2) dx# using partial fractions?
  
• How do you solve the following linear system: # 1/2x+1/3y=13, 3x + 2y = 5 #?
  
• Using the integral test, how do you show whether # (1 + (1/x))^x# diverges or converges?
  
• What is the trigonometric form of #12 e^( ( pi)/2 i ) #?
  
• How do you show whether the improper integral #int dx / [(lnx)^2]# converges or diverges from e to infinity?
  
• How do you factor the trinomial # 49x^2 − 8x + 16#?
  
• How do you factor #n^4 - 1#?
  
• How to integrate ?
  
• How do you find the integral of #int dx/[5x(ln(5x))^2]# from 2 to infinity?
  
• Question #c63da
  
• Question #ad06e
  
• Question #ccfbd
  
• Why is methane a tetrahedral?
  
• How do you simplify #(-28-16i )/( 1-5i)#?
  
• What is the distance between #(-1,7)# and #(4,3)#?
  
• Question #694f3
  
• How do you find #int (3x^2-x)/((1 - x)^2(1 - 3x))dx# using partial fractions?
  
• What is #int 2sec^2xtanxdx#?
  
• What is #int_(0)^(2) x^3*e^(x^2)dx #?
  
• How do you integrate #int (2x-2)/(x^2 - 6x +10)^(1/2)dx# using partial fractions?
  
• What is #int 23/sqrt(13+3x^2) dx#?
  
• How do you simplify #i^102#?
  
• What's the integral of #int sinx * tanxdx#?
  
• What is #int_1^oo 1/((1+x)(x^(1/2)))dx#?
  
• What is #lim_(xrarroo) sin(x)/x #?
  
• How do you integrate #int arctanx/((x^2)(x-1))dx# using partial fractions?
  
• What is #int x^4/(x^4-1)dx#?
  
• How do you integrate #int sin(lnx)# using integration by parts?
  
• What's the integral of #int tan^5(x) dx#?
  
• How do you find the integral of #int x/((x^2 +2)^2) dx# from 0 to infinity?
  
• How do you solve #log_x7 = 1#?
  
• How do you solve # n/n-4/9 - n/n+4/9 = 1/n#?
  
• How do you find the Integral of #(1-x^2)^(3/2)/ (x^6)#?
  
• How do you integrate #(5)/(1+3x)^3#?
  
• How do you find the integral of # dx / (x^2 - 4)^2#?
  
• How do you find the integral of #1/sqrt(x^2 -4)#?
  
• How do you find the integral of #(sqrt(1+x^2)/x)#?
  
• How do you use partial fraction decomposition to decompose the fraction to integrate #3/(x^2-6x+8)#?
  
• How do you integrate #x^2sqrt(x^(4)+5)#?
  
• How do you solve #2/3(a-3)=1/3#?
  
• What is the derivative of #arctan(x-1)#?
  
• What is the derivative of #y = sin(sin(sinx))#?
  
• How do you find the integral of #(1/(e^x+e^-x))dx#?
  
• How do you simplify #sqrt18#?
  
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