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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