Answers edited by Andrea S.

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• How do you find the positive values of p for which `Sigma lnn/n^p` from `[2,oo)` converges?
  
• How do you evaluate the limit `(x^4-10)/(4x^3+x)` as x approaches `oo`?
  
• How do you integrate `1/(e^x(e^x+1))` using partial fractions?
  
• How do you integrate `int (root3x)`?
  
• How do you prove that the integral of ln(sin(x)) on the interval [0, pi/2] is convergent?
  
• How do you use the sum or difference identities to find the exact value of `tan((23pi)/12)`?
  
• How do you find the limit of `sin(x^2−4)/(x−2)` as x approaches 2?
  
• Determine whether the series `sum_(n=1)^oo (2n^2 +3n)/sqrt(5+n^5)` is convergent or divergent. How do i tell which comparison test to use?
  
• How do you use the integral test to determine if `Sigma n^ke^-n` from `[1,oo)` where k is an integer is convergent or divergent?
  
• Sequence ?
  
• How do you evaluate the integral `int 1/(x^2-4)`?
  
• Question #c9fff
  
• How do you find the center and radius of the circle given `3x^2+3y^2+12x-6y+9=0`?
  
• How do you find the power series for `f'(x)` and `int f(t)dt` from [0,x] given the function `f(x)=Sigma 1/n^2x^(2n)` from `n=[1,oo)`?
  
• How do you use the Maclaurin series for `f(x) = ln abs((1+x)/(1-x))`?
  
• How do you use the epsilon delta definition to prove that the limit of `x/(6-x)=1` as `x->3`?
  
• How do you test the improper integral `intx^2 dx` from `(-oo, oo)` and evaluate if possible?
  
• What is the equation of the line normal to `f(x)=sqrt(e^(sqrtx)` at `x=4`?
  
• What is the equation of the line tangent to `f(x)=1/(x^2-4)` at `x=-1`?
  
• How do you integrate `int xsin2x` by parts from `[0,pi]`?
  
• What is a solution to the differential equation `dy/dx=sqrt(xy)sinx`?
  
• Two opposite sides of a parallelogram each have a length of `1`. If one corner of the parallelogram has an angle of `(3 pi)/4` and the parallelogram's area is `4`, how long are the other two sides?
  
• How do you use the limit definition to find the derivative of `f(x)=(2-x)/(3x+1)`?
  
• How do you determine whether the sequence `a_n=ln(ln(n))` converges, if so how do you find the limit?
  
• Question #89694
  
• How do you find an equation of the tangent line to the curve `y=(2x)/(x+1)` at the point (1,1)?
  
• Question #36d91
  
• Question #804a1
  
• What is the domain of `f(x) = arcsin(1-x^2)`?
  
• How do you test the series `Sigma 1/(ln(n!))` from n is `[2,oo)` for convergence?
  
• How do you evaluate `\int \frac { 1} { x ^ { 2} + y ^ { 2} }`?
  
• How do you find the radius of convergence `Sigma (1*4*7* * * (3n+1))/(n!)x^n` from `n=[0,oo)`?
  
• A minimum value of a sinusoidal Function is at `(pi/4, 3)`. The nearest maximum value to the right of this point is at `((7pi)/12, 7)`. What is the equation of this function?
  
• What is the interval of convergence of `sum_1^oo [(2n)!x^n] / ((n^2)! )`?
  
• What are the local extrema of `f(x)= x^3-x+3/x`?
  
• What is the derivative of `-1/(sin(x)^2)`?
  
• What is `f(x) = int xsqrt(3-x) dx` if `f(3) = 0`?
  
• What are the critical points of `g(x)=x/3 + x^-2/3`?
  
• How do you sketch the curve `y=x^3-3x^2-9x+5` by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
  
• What are the points of inflection, if any, of `f(x)=2e^(-x^2)`?
  
• How do you find the derivative of `y=5+sinx`?
  
• How do you find `lim (10x^2+x+2)/(x^3-4x^2-1)` as `x->oo`?
  
• Given `tantheta=-5/12` and `(3pi)/2<theta<2pi`, how do you find `tan(theta/2)`?
  
• How do you use the limit comparison test to determine if `Sigma 1/(n(n^2+1))` from `[1,oo)` is convergent or divergent?
  
• Question #bbb77
  
• How do you show that the series `1+sqrt2+root3(3)+...+rootn(n)+...` diverges?
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph `y=xsqrt(16-x^2)`?
  
• How do you simplify `sin 2x times sin7x`?
  
• Please explain geometric and harmonic progressions?
  
• Question #7bdf4
  
• How do you graph `y=(6x-1)/(3x-1)` using asymptotes, intercepts, end behavior?
  
• How do you determine whether the graph of `f(x)=1/(5x)-x^19` is symmetric with respect to the origin?
  
• What is the area below the curve `f(x)=x^3 -4x^2 +2x+ 8` and bounded by the y-axis, the x axis and x=3 expressed as an integral?
  
• What is the equation of the tangent line of `f(x)=3/(2x+4)` at `x=-1`?
  
• How do you evaluate the integral `int dx/(2x-7)`?
  
• Question #50ca2
  
• Question #dfe82
  
• How do you determine the convergence or divergence of `Sigma 1/ncosnpi` from `[1,oo)`?
  
• Question #ae7e8
  
• What is `f(x) = int 3x dx` if `f(2) = 7`?
  
• How do you use the first and second derivatives to sketch `y = x - ln |x|`?
  
• What is the equation of the line normal to `f(x)=6x^3-8` at `x=7`?
  
• How do you find the local max and min for `x^5 ln x`?
  
• Find the derivative using first principles? : `sin sqrt(x)`
  
• How do you find MacLaurin's Formula for `f(x)=sin(2x)` and use it to approximate `f(1/2)` within 0.01?
  
• How to find the sum of the series `sum_"n=0"^oo(z^(4n)/((4n)!))` when |z| < 1 ?
  
• How do you integrate `int xsqrt(3 + x^2)dx` using trigonometric substitution?
  
• What is the domain and range of `y =arccos(sin(2x))`?
  
• How do you test the series `Sigma sqrt(n+1)-sqrtn` from n is `[0,oo)` for convergence?
  
• How do you apply the ratio test to determine if `Sigma 1/(ln(lnn))^n` from `n=[3,oo)` is convergent to divergent?
  
• Question #95baf
  
• A man repays a loan of $3250 by paying $20 in the first month and then increases the payment by $15 every month. How long will it take him to clear the loan?
  
• Find the roots of `z^5+1=0`?
  
• Question #2f21a
  
• How do you integrate `int 1/(x^3 +4x) dx` using partial fractions?
  
• How do you factor `f(x)=x^3-12x^2+36x-32` completely, given that (x-2) is a factor?
  
• Question #7bf46
  
• Which curve is this? Analytical geometry
  
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